Numeric.SpecFunctions:incompleteBetaApprox from math-functions-0.1.5.2, B

Percentage Accurate: 96.5% → 99.2%

Time: 19.3s

Alternatives: 30

Speedup: 1.5×

• 40.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (* x (exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return x * exp(((y * (log(z) - t)) + (a * (log((1.0 - z)) - b))));
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = x * exp(((y * (log(z) - t)) + (a * (log((1.0d0 - z)) - b))))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return x * Math.exp(((y * (Math.log(z) - t)) + (a * (Math.log((1.0 - z)) - b))));
}

Python

def code(x, y, z, t, a, b):
	return x * math.exp(((y * (math.log(z) - t)) + (a * (math.log((1.0 - z)) - b))))

Julia

function code(x, y, z, t, a, b)
	return Float64(x * exp(Float64(Float64(y * Float64(log(z) - t)) + Float64(a * Float64(log(Float64(1.0 - z)) - b)))))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x * exp(((y * (log(z) - t)) + (a * (log((1.0 - z)) - b))));
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x * N[Exp[N[(N[(y * N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision] + N[(a * N[(N[Log[N[(1.0 - z), $MachinePrecision]], $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Initial Program: 96.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (* x (exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return x * exp(((y * (log(z) - t)) + (a * (log((1.0 - z)) - b))));
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = x * exp(((y * (log(z) - t)) + (a * (log((1.0d0 - z)) - b))))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return x * Math.exp(((y * (Math.log(z) - t)) + (a * (Math.log((1.0 - z)) - b))));
}

Python

def code(x, y, z, t, a, b):
	return x * math.exp(((y * (math.log(z) - t)) + (a * (math.log((1.0 - z)) - b))))

Julia

function code(x, y, z, t, a, b)
	return Float64(x * exp(Float64(Float64(y * Float64(log(z) - t)) + Float64(a * Float64(log(Float64(1.0 - z)) - b)))))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x * exp(((y * (log(z) - t)) + (a * (log((1.0 - z)) - b))));
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x * N[Exp[N[(N[(y * N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision] + N[(a * N[(N[Log[N[(1.0 - z), $MachinePrecision]], $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \frac{x}{e^{y \cdot \left(t - \log z\right) + a \cdot \left(z + b\right)}} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (/ x (exp (+ (* y (- t (log z))) (* a (+ z b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return x / exp(((y * (t - log(z))) + (a * (z + b))));
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = x / exp(((y * (t - log(z))) + (a * (z + b))))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return x / Math.exp(((y * (t - Math.log(z))) + (a * (z + b))));
}

Python

def code(x, y, z, t, a, b):
	return x / math.exp(((y * (t - math.log(z))) + (a * (z + b))))

Julia

function code(x, y, z, t, a, b)
	return Float64(x / exp(Float64(Float64(y * Float64(t - log(z))) + Float64(a * Float64(z + b)))))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x / exp(((y * (t - log(z))) + (a * (z + b))));
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x / N[Exp[N[(N[(y * N[(t - N[Log[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(z + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 96.2%

   \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

3. Simplified 96.2%

   \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
4. Add Preprocessing

5. Taylor expanded in z around 0

   \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(a \cdot b + \left(a \cdot z + y \cdot \left(t - \log z\right)\right)\right)}\right)\right) \]
6. Step-by-step derivation

   1. associate-+r+ N/A

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\left(\left(a \cdot b + a \cdot z\right) + y \cdot \left(t - \log z\right)\right)\right)\right) \]

   2. +-commutative N/A

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\left(y \cdot \left(t - \log z\right) + \left(a \cdot b + a \cdot z\right)\right)\right)\right) \]

   3. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{+.f64}\left(\left(y \cdot \left(t - \log z\right)\right), \left(a \cdot b + a \cdot z\right)\right)\right)\right) \]

   4. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \left(t - \log z\right)\right), \left(a \cdot b + a \cdot z\right)\right)\right)\right) \]

   5. --lowering--.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, \log z\right)\right), \left(a \cdot b + a \cdot z\right)\right)\right)\right) \]

   6. log-lowering-log.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, \mathsf{log.f64}\left(z\right)\right)\right), \left(a \cdot b + a \cdot z\right)\right)\right)\right) \]

   7. distribute-lft-out N/A

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, \mathsf{log.f64}\left(z\right)\right)\right), \left(a \cdot \left(b + z\right)\right)\right)\right)\right) \]

   8. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, \mathsf{log.f64}\left(z\right)\right)\right), \mathsf{*.f64}\left(a, \left(b + z\right)\right)\right)\right)\right) \]

   9. +-lowering-+.f64 100.0%

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, \mathsf{log.f64}\left(z\right)\right)\right), \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(b, z\right)\right)\right)\right)\right) \]

7. Simplified 100.0%

   \[\leadsto \frac{x}{e^{\color{blue}{y \cdot \left(t - \log z\right) + a \cdot \left(b + z\right)}}} \]

8. Final simplification 100.0%

   \[\leadsto \frac{x}{e^{y \cdot \left(t - \log z\right) + a \cdot \left(z + b\right)}} \]
9. Add Preprocessing

Alternative 2: 83.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{e^{y \cdot \left(t - \log z\right)}}\\ \mathbf{if}\;y \leq -2.5 \cdot 10^{-56}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-120}:\\ \;\;\;\;\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (exp (* y (- t (log z)))))))
   (if (<= y -2.5e-56)
     t_1
     (if (<= y 4.4e-120) (/ x (exp (* a (- b (log (- 1.0 z)))))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / exp((y * (t - log(z))));
	double tmp;
	if (y <= -2.5e-56) {
		tmp = t_1;
	} else if (y <= 4.4e-120) {
		tmp = x / exp((a * (b - log((1.0 - z)))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / exp((y * (t - log(z))))
    if (y <= (-2.5d-56)) then
        tmp = t_1
    else if (y <= 4.4d-120) then
        tmp = x / exp((a * (b - log((1.0d0 - z)))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / Math.exp((y * (t - Math.log(z))));
	double tmp;
	if (y <= -2.5e-56) {
		tmp = t_1;
	} else if (y <= 4.4e-120) {
		tmp = x / Math.exp((a * (b - Math.log((1.0 - z)))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / math.exp((y * (t - math.log(z))))
	tmp = 0
	if y <= -2.5e-56:
		tmp = t_1
	elif y <= 4.4e-120:
		tmp = x / math.exp((a * (b - math.log((1.0 - z)))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / exp(Float64(y * Float64(t - log(z)))))
	tmp = 0.0
	if (y <= -2.5e-56)
		tmp = t_1;
	elseif (y <= 4.4e-120)
		tmp = Float64(x / exp(Float64(a * Float64(b - log(Float64(1.0 - z))))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / exp((y * (t - log(z))));
	tmp = 0.0;
	if (y <= -2.5e-56)
		tmp = t_1;
	elseif (y <= 4.4e-120)
		tmp = x / exp((a * (b - log((1.0 - z)))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[Exp[N[(y * N[(t - N[Log[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.5e-56], t$95$1, If[LessEqual[y, 4.4e-120], N[(x / N[Exp[N[(a * N[(b - N[Log[N[(1.0 - z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.49999999999999999e-56 or 4.40000000000000025e-120 < y

   1. Initial program 98.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 98.0%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in a around 0

      \[\leadsto \color{blue}{\frac{x}{e^{y \cdot \left(t - \log z\right)}}} \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(e^{y \cdot \left(t - \log z\right)}\right)}\right) \]

      2. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\left(y \cdot \left(t - \log z\right)\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, \left(t - \log z\right)\right)\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, \log z\right)\right)\right)\right) \]

      5. log-lowering-log.f64 86.9%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, \mathsf{log.f64}\left(z\right)\right)\right)\right)\right) \]

   7. Simplified 86.9%

      \[\leadsto \color{blue}{\frac{x}{e^{y \cdot \left(t - \log z\right)}}} \]

   if -2.49999999999999999e-56 < y < 4.40000000000000025e-120

   1. Initial program 93.4%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 93.4%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right)}}} \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(e^{a \cdot \left(b - \log \left(1 - z\right)\right)}\right)}\right) \]

      2. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\left(a \cdot \left(b - \log \left(1 - z\right)\right)\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, \left(b - \log \left(1 - z\right)\right)\right)\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(b, \log \left(1 - z\right)\right)\right)\right)\right) \]

      5. log-lowering-log.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(b, \mathsf{log.f64}\left(\left(1 - z\right)\right)\right)\right)\right)\right) \]

      6. --lowering--.f64 83.3%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, \mathsf{\_.f64}\left(b, \mathsf{log.f64}\left(\mathsf{\_.f64}\left(1, z\right)\right)\right)\right)\right)\right) \]

   7. Simplified 83.3%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right)}}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 83.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{e^{y \cdot \left(t - \log z\right)}}\\ \mathbf{if}\;y \leq -6.5 \cdot 10^{-56}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-120}:\\ \;\;\;\;\frac{x}{e^{a \cdot b}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (exp (* y (- t (log z)))))))
   (if (<= y -6.5e-56) t_1 (if (<= y 6.5e-120) (/ x (exp (* a b))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / exp((y * (t - log(z))));
	double tmp;
	if (y <= -6.5e-56) {
		tmp = t_1;
	} else if (y <= 6.5e-120) {
		tmp = x / exp((a * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / exp((y * (t - log(z))))
    if (y <= (-6.5d-56)) then
        tmp = t_1
    else if (y <= 6.5d-120) then
        tmp = x / exp((a * b))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / Math.exp((y * (t - Math.log(z))));
	double tmp;
	if (y <= -6.5e-56) {
		tmp = t_1;
	} else if (y <= 6.5e-120) {
		tmp = x / Math.exp((a * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / math.exp((y * (t - math.log(z))))
	tmp = 0
	if y <= -6.5e-56:
		tmp = t_1
	elif y <= 6.5e-120:
		tmp = x / math.exp((a * b))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / exp(Float64(y * Float64(t - log(z)))))
	tmp = 0.0
	if (y <= -6.5e-56)
		tmp = t_1;
	elseif (y <= 6.5e-120)
		tmp = Float64(x / exp(Float64(a * b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / exp((y * (t - log(z))));
	tmp = 0.0;
	if (y <= -6.5e-56)
		tmp = t_1;
	elseif (y <= 6.5e-120)
		tmp = x / exp((a * b));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[Exp[N[(y * N[(t - N[Log[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.5e-56], t$95$1, If[LessEqual[y, 6.5e-120], N[(x / N[Exp[N[(a * b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -6.4999999999999997e-56 or 6.50000000000000029e-120 < y

   1. Initial program 98.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 98.0%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in a around 0

      \[\leadsto \color{blue}{\frac{x}{e^{y \cdot \left(t - \log z\right)}}} \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(e^{y \cdot \left(t - \log z\right)}\right)}\right) \]

      2. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\left(y \cdot \left(t - \log z\right)\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, \left(t - \log z\right)\right)\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, \log z\right)\right)\right)\right) \]

      5. log-lowering-log.f64 86.9%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, \mathsf{log.f64}\left(z\right)\right)\right)\right)\right) \]

   7. Simplified 86.9%

      \[\leadsto \color{blue}{\frac{x}{e^{y \cdot \left(t - \log z\right)}}} \]

   if -6.4999999999999997e-56 < y < 6.50000000000000029e-120

   1. Initial program 93.4%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 93.4%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(a \cdot b\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 82.4%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, b\right)\right)\right) \]

   7. Simplified 82.4%

      \[\leadsto \frac{x}{e^{\color{blue}{a \cdot b}}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 54.8% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.5 \cdot \left(a \cdot a\right)\\ t_2 := x \cdot {z}^{y}\\ t_3 := \left(t \cdot t\right) \cdot 0.5\\ \mathbf{if}\;y \leq -8.2 \cdot 10^{+174}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{+76}:\\ \;\;\;\;\frac{x}{y \cdot \left(t + y \cdot \left(0.16666666666666666 \cdot \left(y \cdot \left(t \cdot \left(t \cdot t\right)\right)\right) + t\_3\right)\right) + 1}\\ \mathbf{elif}\;y \leq -2400:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-200}:\\ \;\;\;\;\frac{x}{b \cdot \left(a + b \cdot \left(0.16666666666666666 \cdot \left(b \cdot \left(a \cdot \left(a \cdot a\right)\right)\right) + t\_1\right)\right) + 1}\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-133}:\\ \;\;\;\;x + b \cdot \left(b \cdot \left(x \cdot t\_1\right) - x \cdot a\right)\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-12}:\\ \;\;\;\;\left(y \cdot y\right) \cdot \left(x \cdot t\_3 + \frac{\frac{x}{y} - x \cdot t}{y}\right)\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+282}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \left(t \cdot \left(\left(x \cdot 0.5\right) \cdot \left(y \cdot y\right)\right) - x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* 0.5 (* a a))) (t_2 (* x (pow z y))) (t_3 (* (* t t) 0.5)))
   (if (<= y -8.2e+174)
     t_2
     (if (<= y -4.5e+76)
       (/
        x
        (+
         (* y (+ t (* y (+ (* 0.16666666666666666 (* y (* t (* t t)))) t_3))))
         1.0))
       (if (<= y -2400.0)
         t_2
         (if (<= y -2.5e-200)
           (/
            x
            (+
             (*
              b
              (+ a (* b (+ (* 0.16666666666666666 (* b (* a (* a a)))) t_1))))
             1.0))
           (if (<= y 1.65e-133)
             (+ x (* b (- (* b (* x t_1)) (* x a))))
             (if (<= y 2.5e-12)
               (* (* y y) (+ (* x t_3) (/ (- (/ x y) (* x t)) y)))
               (if (<= y 6.8e+282)
                 t_2
                 (+ x (* t (- (* t (* (* x 0.5) (* y y))) (* x y)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 0.5 * (a * a);
	double t_2 = x * pow(z, y);
	double t_3 = (t * t) * 0.5;
	double tmp;
	if (y <= -8.2e+174) {
		tmp = t_2;
	} else if (y <= -4.5e+76) {
		tmp = x / ((y * (t + (y * ((0.16666666666666666 * (y * (t * (t * t)))) + t_3)))) + 1.0);
	} else if (y <= -2400.0) {
		tmp = t_2;
	} else if (y <= -2.5e-200) {
		tmp = x / ((b * (a + (b * ((0.16666666666666666 * (b * (a * (a * a)))) + t_1)))) + 1.0);
	} else if (y <= 1.65e-133) {
		tmp = x + (b * ((b * (x * t_1)) - (x * a)));
	} else if (y <= 2.5e-12) {
		tmp = (y * y) * ((x * t_3) + (((x / y) - (x * t)) / y));
	} else if (y <= 6.8e+282) {
		tmp = t_2;
	} else {
		tmp = x + (t * ((t * ((x * 0.5) * (y * y))) - (x * y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = 0.5d0 * (a * a)
    t_2 = x * (z ** y)
    t_3 = (t * t) * 0.5d0
    if (y <= (-8.2d+174)) then
        tmp = t_2
    else if (y <= (-4.5d+76)) then
        tmp = x / ((y * (t + (y * ((0.16666666666666666d0 * (y * (t * (t * t)))) + t_3)))) + 1.0d0)
    else if (y <= (-2400.0d0)) then
        tmp = t_2
    else if (y <= (-2.5d-200)) then
        tmp = x / ((b * (a + (b * ((0.16666666666666666d0 * (b * (a * (a * a)))) + t_1)))) + 1.0d0)
    else if (y <= 1.65d-133) then
        tmp = x + (b * ((b * (x * t_1)) - (x * a)))
    else if (y <= 2.5d-12) then
        tmp = (y * y) * ((x * t_3) + (((x / y) - (x * t)) / y))
    else if (y <= 6.8d+282) then
        tmp = t_2
    else
        tmp = x + (t * ((t * ((x * 0.5d0) * (y * y))) - (x * y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 0.5 * (a * a);
	double t_2 = x * Math.pow(z, y);
	double t_3 = (t * t) * 0.5;
	double tmp;
	if (y <= -8.2e+174) {
		tmp = t_2;
	} else if (y <= -4.5e+76) {
		tmp = x / ((y * (t + (y * ((0.16666666666666666 * (y * (t * (t * t)))) + t_3)))) + 1.0);
	} else if (y <= -2400.0) {
		tmp = t_2;
	} else if (y <= -2.5e-200) {
		tmp = x / ((b * (a + (b * ((0.16666666666666666 * (b * (a * (a * a)))) + t_1)))) + 1.0);
	} else if (y <= 1.65e-133) {
		tmp = x + (b * ((b * (x * t_1)) - (x * a)));
	} else if (y <= 2.5e-12) {
		tmp = (y * y) * ((x * t_3) + (((x / y) - (x * t)) / y));
	} else if (y <= 6.8e+282) {
		tmp = t_2;
	} else {
		tmp = x + (t * ((t * ((x * 0.5) * (y * y))) - (x * y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = 0.5 * (a * a)
	t_2 = x * math.pow(z, y)
	t_3 = (t * t) * 0.5
	tmp = 0
	if y <= -8.2e+174:
		tmp = t_2
	elif y <= -4.5e+76:
		tmp = x / ((y * (t + (y * ((0.16666666666666666 * (y * (t * (t * t)))) + t_3)))) + 1.0)
	elif y <= -2400.0:
		tmp = t_2
	elif y <= -2.5e-200:
		tmp = x / ((b * (a + (b * ((0.16666666666666666 * (b * (a * (a * a)))) + t_1)))) + 1.0)
	elif y <= 1.65e-133:
		tmp = x + (b * ((b * (x * t_1)) - (x * a)))
	elif y <= 2.5e-12:
		tmp = (y * y) * ((x * t_3) + (((x / y) - (x * t)) / y))
	elif y <= 6.8e+282:
		tmp = t_2
	else:
		tmp = x + (t * ((t * ((x * 0.5) * (y * y))) - (x * y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(0.5 * Float64(a * a))
	t_2 = Float64(x * (z ^ y))
	t_3 = Float64(Float64(t * t) * 0.5)
	tmp = 0.0
	if (y <= -8.2e+174)
		tmp = t_2;
	elseif (y <= -4.5e+76)
		tmp = Float64(x / Float64(Float64(y * Float64(t + Float64(y * Float64(Float64(0.16666666666666666 * Float64(y * Float64(t * Float64(t * t)))) + t_3)))) + 1.0));
	elseif (y <= -2400.0)
		tmp = t_2;
	elseif (y <= -2.5e-200)
		tmp = Float64(x / Float64(Float64(b * Float64(a + Float64(b * Float64(Float64(0.16666666666666666 * Float64(b * Float64(a * Float64(a * a)))) + t_1)))) + 1.0));
	elseif (y <= 1.65e-133)
		tmp = Float64(x + Float64(b * Float64(Float64(b * Float64(x * t_1)) - Float64(x * a))));
	elseif (y <= 2.5e-12)
		tmp = Float64(Float64(y * y) * Float64(Float64(x * t_3) + Float64(Float64(Float64(x / y) - Float64(x * t)) / y)));
	elseif (y <= 6.8e+282)
		tmp = t_2;
	else
		tmp = Float64(x + Float64(t * Float64(Float64(t * Float64(Float64(x * 0.5) * Float64(y * y))) - Float64(x * y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 0.5 * (a * a);
	t_2 = x * (z ^ y);
	t_3 = (t * t) * 0.5;
	tmp = 0.0;
	if (y <= -8.2e+174)
		tmp = t_2;
	elseif (y <= -4.5e+76)
		tmp = x / ((y * (t + (y * ((0.16666666666666666 * (y * (t * (t * t)))) + t_3)))) + 1.0);
	elseif (y <= -2400.0)
		tmp = t_2;
	elseif (y <= -2.5e-200)
		tmp = x / ((b * (a + (b * ((0.16666666666666666 * (b * (a * (a * a)))) + t_1)))) + 1.0);
	elseif (y <= 1.65e-133)
		tmp = x + (b * ((b * (x * t_1)) - (x * a)));
	elseif (y <= 2.5e-12)
		tmp = (y * y) * ((x * t_3) + (((x / y) - (x * t)) / y));
	elseif (y <= 6.8e+282)
		tmp = t_2;
	else
		tmp = x + (t * ((t * ((x * 0.5) * (y * y))) - (x * y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(0.5 * N[(a * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t * t), $MachinePrecision] * 0.5), $MachinePrecision]}, If[LessEqual[y, -8.2e+174], t$95$2, If[LessEqual[y, -4.5e+76], N[(x / N[(N[(y * N[(t + N[(y * N[(N[(0.16666666666666666 * N[(y * N[(t * N[(t * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2400.0], t$95$2, If[LessEqual[y, -2.5e-200], N[(x / N[(N[(b * N[(a + N[(b * N[(N[(0.16666666666666666 * N[(b * N[(a * N[(a * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.65e-133], N[(x + N[(b * N[(N[(b * N[(x * t$95$1), $MachinePrecision]), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.5e-12], N[(N[(y * y), $MachinePrecision] * N[(N[(x * t$95$3), $MachinePrecision] + N[(N[(N[(x / y), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.8e+282], t$95$2, N[(x + N[(t * N[(N[(t * N[(N[(x * 0.5), $MachinePrecision] * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -8.20000000000000061e174 or -4.4999999999999997e76 < y < -2400 or 2.49999999999999985e-12 < y < 6.80000000000000048e282

   1. Initial program 98.9%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 99.0%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in a around 0

      \[\leadsto \color{blue}{\frac{x}{e^{y \cdot \left(t - \log z\right)}}} \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(e^{y \cdot \left(t - \log z\right)}\right)}\right) \]

      2. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\left(y \cdot \left(t - \log z\right)\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, \left(t - \log z\right)\right)\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, \log z\right)\right)\right)\right) \]

      5. log-lowering-log.f64 89.6%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, \mathsf{log.f64}\left(z\right)\right)\right)\right)\right) \]

   7. Simplified 89.6%

      \[\leadsto \color{blue}{\frac{x}{e^{y \cdot \left(t - \log z\right)}}} \]

   8. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\frac{x}{e^{-1 \cdot \left(y \cdot \log z\right)}}} \]
   9. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(e^{-1 \cdot \left(y \cdot \log z\right)}\right)}\right) \]

      2. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(e^{\mathsf{neg}\left(y \cdot \log z\right)}\right)\right) \]

      3. exp-neg N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(\frac{1}{\color{blue}{e^{y \cdot \log z}}}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(1, \color{blue}{\left(e^{y \cdot \log z}\right)}\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(1, \left(e^{\log z \cdot y}\right)\right)\right) \]

      6. exp-to-pow N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(1, \left({z}^{\color{blue}{y}}\right)\right)\right) \]

      7. pow-lowering-pow.f64 74.1%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(1, \mathsf{pow.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

   10. Simplified 74.1%

       \[\leadsto \color{blue}{\frac{x}{\frac{1}{{z}^{y}}}} \]
   11. Step-by-step derivation

       1. associate-/r/ N/A

          \[\leadsto \frac{x}{1} \cdot \color{blue}{{z}^{y}} \]

       2. /-rgt-identity N/A

          \[\leadsto x \cdot {\color{blue}{z}}^{y} \]

       3. *-commutative N/A

          \[\leadsto {z}^{y} \cdot \color{blue}{x} \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left({z}^{y}\right), \color{blue}{x}\right) \]

       5. pow-lowering-pow.f64 74.1%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{pow.f64}\left(z, y\right), x\right) \]

   12. Applied egg-rr 74.1%

       \[\leadsto \color{blue}{{z}^{y} \cdot x} \]

   if -8.20000000000000061e174 < y < -4.4999999999999997e76

   1. Initial program 100.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(t \cdot y\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\left(y \cdot t\right)\right)\right) \]

      2. *-lowering-*.f64 82.8%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, t\right)\right)\right) \]

   7. Simplified 82.8%

      \[\leadsto \frac{x}{e^{\color{blue}{y \cdot t}}} \]

   8. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + y \cdot \left(t + y \cdot \left(\frac{1}{6} \cdot \left({t}^{3} \cdot y\right) + \frac{1}{2} \cdot {t}^{2}\right)\right)\right)}\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(y \cdot \left(t + y \cdot \left(\frac{1}{6} \cdot \left({t}^{3} \cdot y\right) + \frac{1}{2} \cdot {t}^{2}\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \color{blue}{\left(t + y \cdot \left(\frac{1}{6} \cdot \left({t}^{3} \cdot y\right) + \frac{1}{2} \cdot {t}^{2}\right)\right)}\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \color{blue}{\left(y \cdot \left(\frac{1}{6} \cdot \left({t}^{3} \cdot y\right) + \frac{1}{2} \cdot {t}^{2}\right)\right)}\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{1}{6} \cdot \left({t}^{3} \cdot y\right) + \frac{1}{2} \cdot {t}^{2}\right)}\right)\right)\right)\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\left(\frac{1}{6} \cdot \left({t}^{3} \cdot y\right)\right), \color{blue}{\left(\frac{1}{2} \cdot {t}^{2}\right)}\right)\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, \left({t}^{3} \cdot y\right)\right), \left(\color{blue}{\frac{1}{2}} \cdot {t}^{2}\right)\right)\right)\right)\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, \left(y \cdot {t}^{3}\right)\right), \left(\frac{1}{2} \cdot {t}^{2}\right)\right)\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, \mathsf{*.f64}\left(y, \left({t}^{3}\right)\right)\right), \left(\frac{1}{2} \cdot {t}^{2}\right)\right)\right)\right)\right)\right)\right) \]

      9. cube-mult N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, \mathsf{*.f64}\left(y, \left(t \cdot \left(t \cdot t\right)\right)\right)\right), \left(\frac{1}{2} \cdot {t}^{2}\right)\right)\right)\right)\right)\right)\right) \]

      10. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, \mathsf{*.f64}\left(y, \left(t \cdot {t}^{2}\right)\right)\right), \left(\frac{1}{2} \cdot {t}^{2}\right)\right)\right)\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \left({t}^{2}\right)\right)\right)\right), \left(\frac{1}{2} \cdot {t}^{2}\right)\right)\right)\right)\right)\right)\right) \]

      12. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \left(t \cdot t\right)\right)\right)\right), \left(\frac{1}{2} \cdot {t}^{2}\right)\right)\right)\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(t, t\right)\right)\right)\right), \left(\frac{1}{2} \cdot {t}^{2}\right)\right)\right)\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(t, t\right)\right)\right)\right), \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{\left({t}^{2}\right)}\right)\right)\right)\right)\right)\right)\right) \]

      15. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(t, t\right)\right)\right)\right), \mathsf{*.f64}\left(\frac{1}{2}, \left(t \cdot \color{blue}{t}\right)\right)\right)\right)\right)\right)\right)\right) \]

      16. *-lowering-*.f64 77.3%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(t, t\right)\right)\right)\right), \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(t, \color{blue}{t}\right)\right)\right)\right)\right)\right)\right)\right) \]

   10. Simplified 77.3%

       \[\leadsto \frac{x}{\color{blue}{1 + y \cdot \left(t + y \cdot \left(0.16666666666666666 \cdot \left(y \cdot \left(t \cdot \left(t \cdot t\right)\right)\right) + 0.5 \cdot \left(t \cdot t\right)\right)\right)}} \]

   if -2400 < y < -2.49999999999999996e-200

   1. Initial program 91.8%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 91.8%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(a \cdot b\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 61.1%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, b\right)\right)\right) \]

   7. Simplified 61.1%

      \[\leadsto \frac{x}{e^{\color{blue}{a \cdot b}}} \]

   8. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + b \cdot \left(a + b \cdot \left(\frac{1}{6} \cdot \left({a}^{3} \cdot b\right) + \frac{1}{2} \cdot {a}^{2}\right)\right)\right)}\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(b \cdot \left(a + b \cdot \left(\frac{1}{6} \cdot \left({a}^{3} \cdot b\right) + \frac{1}{2} \cdot {a}^{2}\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \color{blue}{\left(a + b \cdot \left(\frac{1}{6} \cdot \left({a}^{3} \cdot b\right) + \frac{1}{2} \cdot {a}^{2}\right)\right)}\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \color{blue}{\left(b \cdot \left(\frac{1}{6} \cdot \left({a}^{3} \cdot b\right) + \frac{1}{2} \cdot {a}^{2}\right)\right)}\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \color{blue}{\left(\frac{1}{6} \cdot \left({a}^{3} \cdot b\right) + \frac{1}{2} \cdot {a}^{2}\right)}\right)\right)\right)\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\left(\frac{1}{6} \cdot \left({a}^{3} \cdot b\right)\right), \color{blue}{\left(\frac{1}{2} \cdot {a}^{2}\right)}\right)\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, \left({a}^{3} \cdot b\right)\right), \left(\color{blue}{\frac{1}{2}} \cdot {a}^{2}\right)\right)\right)\right)\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, \left(b \cdot {a}^{3}\right)\right), \left(\frac{1}{2} \cdot {a}^{2}\right)\right)\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, \mathsf{*.f64}\left(b, \left({a}^{3}\right)\right)\right), \left(\frac{1}{2} \cdot {a}^{2}\right)\right)\right)\right)\right)\right)\right) \]

      9. cube-mult N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, \mathsf{*.f64}\left(b, \left(a \cdot \left(a \cdot a\right)\right)\right)\right), \left(\frac{1}{2} \cdot {a}^{2}\right)\right)\right)\right)\right)\right)\right) \]

      10. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, \mathsf{*.f64}\left(b, \left(a \cdot {a}^{2}\right)\right)\right), \left(\frac{1}{2} \cdot {a}^{2}\right)\right)\right)\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \left({a}^{2}\right)\right)\right)\right), \left(\frac{1}{2} \cdot {a}^{2}\right)\right)\right)\right)\right)\right)\right) \]

      12. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \left(a \cdot a\right)\right)\right)\right), \left(\frac{1}{2} \cdot {a}^{2}\right)\right)\right)\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(a, a\right)\right)\right)\right), \left(\frac{1}{2} \cdot {a}^{2}\right)\right)\right)\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(a, a\right)\right)\right)\right), \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{\left({a}^{2}\right)}\right)\right)\right)\right)\right)\right)\right) \]

      15. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(a, a\right)\right)\right)\right), \mathsf{*.f64}\left(\frac{1}{2}, \left(a \cdot \color{blue}{a}\right)\right)\right)\right)\right)\right)\right)\right) \]

      16. *-lowering-*.f64 54.6%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(a, a\right)\right)\right)\right), \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(a, \color{blue}{a}\right)\right)\right)\right)\right)\right)\right)\right) \]

   10. Simplified 54.6%

       \[\leadsto \frac{x}{\color{blue}{1 + b \cdot \left(a + b \cdot \left(0.16666666666666666 \cdot \left(b \cdot \left(a \cdot \left(a \cdot a\right)\right)\right) + 0.5 \cdot \left(a \cdot a\right)\right)\right)}} \]

   if -2.49999999999999996e-200 < y < 1.65000000000000005e-133

   1. Initial program 94.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 94.0%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(a \cdot b\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 89.6%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, b\right)\right)\right) \]

   7. Simplified 89.6%

      \[\leadsto \frac{x}{e^{\color{blue}{a \cdot b}}} \]

   8. Taylor expanded in b around 0

      \[\leadsto \color{blue}{x + b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left({a}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({a}^{2} \cdot x\right)\right)\right) - a \cdot x\right)} \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left({a}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({a}^{2} \cdot x\right)\right)\right) - a \cdot x\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \color{blue}{\left(-1 \cdot \left(b \cdot \left(-1 \cdot \left({a}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({a}^{2} \cdot x\right)\right)\right) - a \cdot x\right)}\right)\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(\left(\mathsf{neg}\left(b \cdot \left(-1 \cdot \left({a}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({a}^{2} \cdot x\right)\right)\right)\right) - \color{blue}{a} \cdot x\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(b \cdot \left(\mathsf{neg}\left(\left(-1 \cdot \left({a}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({a}^{2} \cdot x\right)\right)\right)\right) - \color{blue}{a} \cdot x\right)\right)\right) \]

      5. distribute-rgt-out N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(b \cdot \left(\mathsf{neg}\left(\left({a}^{2} \cdot x\right) \cdot \left(-1 + \frac{1}{2}\right)\right)\right) - a \cdot x\right)\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(b \cdot \left(\mathsf{neg}\left(\left({a}^{2} \cdot x\right) \cdot \frac{-1}{2}\right)\right) - a \cdot x\right)\right)\right) \]

      7. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(b \cdot \left(\left({a}^{2} \cdot x\right) \cdot \left(\mathsf{neg}\left(\frac{-1}{2}\right)\right)\right) - a \cdot x\right)\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(b \cdot \left(\left({a}^{2} \cdot x\right) \cdot \frac{1}{2}\right) - a \cdot x\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(b \cdot \left(\frac{1}{2} \cdot \left({a}^{2} \cdot x\right)\right) - a \cdot x\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(b \cdot \left(\frac{1}{2} \cdot \left({a}^{2} \cdot x\right)\right)\right), \color{blue}{\left(a \cdot x\right)}\right)\right)\right) \]

   10. Simplified 67.1%

       \[\leadsto \color{blue}{x + b \cdot \left(b \cdot \left(\left(0.5 \cdot \left(a \cdot a\right)\right) \cdot x\right) - x \cdot a\right)} \]

   if 1.65000000000000005e-133 < y < 2.49999999999999985e-12

   1. Initial program 96.1%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 96.1%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(t \cdot y\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\left(y \cdot t\right)\right)\right) \]

      2. *-lowering-*.f64 67.3%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, t\right)\right)\right) \]

   7. Simplified 67.3%

      \[\leadsto \frac{x}{e^{\color{blue}{y \cdot t}}} \]

   8. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x + y \cdot \left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) - t \cdot x\right)} \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot \left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) - t \cdot x\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) - t \cdot x\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right)\right), \color{blue}{\left(t \cdot x\right)}\right)\right)\right) \]

   10. Simplified 59.3%

       \[\leadsto \color{blue}{x + y \cdot \left(y \cdot \left(0.5 \cdot \left(x \cdot \left(t \cdot t\right)\right)\right) - x \cdot t\right)} \]

   11. Taylor expanded in y around -inf

       \[\leadsto \color{blue}{{y}^{2} \cdot \left(-1 \cdot \frac{-1 \cdot \frac{x}{y} + t \cdot x}{y} + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)} \]
   12. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left({y}^{2}\right), \color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{x}{y} + t \cdot x}{y} + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)}\right) \]

       2. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(y \cdot y\right), \left(\color{blue}{-1 \cdot \frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}} + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \left(\color{blue}{-1 \cdot \frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}} + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) \]

       4. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right) + \color{blue}{-1 \cdot \frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}}\right)\right) \]

       5. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right) + \left(\mathsf{neg}\left(\frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}\right)\right)\right)\right) \]

       6. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right) - \color{blue}{\frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}}\right)\right) \]

       7. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right), \color{blue}{\left(\frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}\right)}\right)\right) \]

       8. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\left(\left({t}^{2} \cdot x\right) \cdot \frac{1}{2}\right), \left(\frac{\color{blue}{-1 \cdot \frac{x}{y} + t \cdot x}}{y}\right)\right)\right) \]

       9. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\left(\left(x \cdot {t}^{2}\right) \cdot \frac{1}{2}\right), \left(\frac{\color{blue}{-1 \cdot \frac{x}{y}} + t \cdot x}{y}\right)\right)\right) \]

       10. associate-*l* N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\left(x \cdot \left({t}^{2} \cdot \frac{1}{2}\right)\right), \left(\frac{\color{blue}{-1 \cdot \frac{x}{y} + t \cdot x}}{y}\right)\right)\right) \]

       11. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \left({t}^{2} \cdot \frac{1}{2}\right)\right), \left(\frac{\color{blue}{-1 \cdot \frac{x}{y} + t \cdot x}}{y}\right)\right)\right) \]

       12. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\left({t}^{2}\right), \frac{1}{2}\right)\right), \left(\frac{-1 \cdot \frac{x}{y} + \color{blue}{t \cdot x}}{y}\right)\right)\right) \]

       13. unpow2 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\left(t \cdot t\right), \frac{1}{2}\right)\right), \left(\frac{-1 \cdot \frac{x}{y} + \color{blue}{t} \cdot x}{y}\right)\right)\right) \]

       14. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, t\right), \frac{1}{2}\right)\right), \left(\frac{-1 \cdot \frac{x}{y} + \color{blue}{t} \cdot x}{y}\right)\right)\right) \]

       15. /-lowering-/.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, t\right), \frac{1}{2}\right)\right), \mathsf{/.f64}\left(\left(-1 \cdot \frac{x}{y} + t \cdot x\right), \color{blue}{y}\right)\right)\right) \]

   13. Simplified 66.7%

       \[\leadsto \color{blue}{\left(y \cdot y\right) \cdot \left(x \cdot \left(\left(t \cdot t\right) \cdot 0.5\right) - \frac{x \cdot t - \frac{x}{y}}{y}\right)} \]

   if 6.80000000000000048e282 < y

   1. Initial program 100.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(t \cdot y\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\left(y \cdot t\right)\right)\right) \]

      2. *-lowering-*.f64 100.0%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, t\right)\right)\right) \]

   7. Simplified 100.0%

      \[\leadsto \frac{x}{e^{\color{blue}{y \cdot t}}} \]

   8. Taylor expanded in t around 0

      \[\leadsto \color{blue}{x + t \cdot \left(-1 \cdot \left(t \cdot \left(-1 \cdot \left(x \cdot {y}^{2}\right) + \frac{1}{2} \cdot \left(x \cdot {y}^{2}\right)\right)\right) - x \cdot y\right)} \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(t \cdot \left(-1 \cdot \left(t \cdot \left(-1 \cdot \left(x \cdot {y}^{2}\right) + \frac{1}{2} \cdot \left(x \cdot {y}^{2}\right)\right)\right) - x \cdot y\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(t, \color{blue}{\left(-1 \cdot \left(t \cdot \left(-1 \cdot \left(x \cdot {y}^{2}\right) + \frac{1}{2} \cdot \left(x \cdot {y}^{2}\right)\right)\right) - x \cdot y\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(-1 \cdot \left(t \cdot \left(-1 \cdot \left(x \cdot {y}^{2}\right) + \frac{1}{2} \cdot \left(x \cdot {y}^{2}\right)\right)\right)\right), \color{blue}{\left(x \cdot y\right)}\right)\right)\right) \]

   10. Simplified 100.0%

       \[\leadsto \color{blue}{x + t \cdot \left(t \cdot \left(\left(0.5 \cdot x\right) \cdot \left(y \cdot y\right)\right) - x \cdot y\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+174}:\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{+76}:\\ \;\;\;\;\frac{x}{y \cdot \left(t + y \cdot \left(0.16666666666666666 \cdot \left(y \cdot \left(t \cdot \left(t \cdot t\right)\right)\right) + \left(t \cdot t\right) \cdot 0.5\right)\right) + 1}\\ \mathbf{elif}\;y \leq -2400:\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-200}:\\ \;\;\;\;\frac{x}{b \cdot \left(a + b \cdot \left(0.16666666666666666 \cdot \left(b \cdot \left(a \cdot \left(a \cdot a\right)\right)\right) + 0.5 \cdot \left(a \cdot a\right)\right)\right) + 1}\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-133}:\\ \;\;\;\;x + b \cdot \left(b \cdot \left(x \cdot \left(0.5 \cdot \left(a \cdot a\right)\right)\right) - x \cdot a\right)\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-12}:\\ \;\;\;\;\left(y \cdot y\right) \cdot \left(x \cdot \left(\left(t \cdot t\right) \cdot 0.5\right) + \frac{\frac{x}{y} - x \cdot t}{y}\right)\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+282}:\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \left(t \cdot \left(\left(x \cdot 0.5\right) \cdot \left(y \cdot y\right)\right) - x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 69.1% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot {z}^{y}\\ \mathbf{if}\;y \leq -8.2 \cdot 10^{+174}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{+76}:\\ \;\;\;\;\frac{x}{y \cdot \left(t + y \cdot \left(0.16666666666666666 \cdot \left(y \cdot \left(t \cdot \left(t \cdot t\right)\right)\right) + \left(t \cdot t\right) \cdot 0.5\right)\right) + 1}\\ \mathbf{elif}\;y \leq -2500:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-23}:\\ \;\;\;\;\frac{x}{e^{a \cdot b}}\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+282}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \left(t \cdot \left(\left(x \cdot 0.5\right) \cdot \left(y \cdot y\right)\right) - x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (pow z y))))
   (if (<= y -8.2e+174)
     t_1
     (if (<= y -5.2e+76)
       (/
        x
        (+
         (*
          y
          (+
           t
           (*
            y
            (+ (* 0.16666666666666666 (* y (* t (* t t)))) (* (* t t) 0.5)))))
         1.0))
       (if (<= y -2500.0)
         t_1
         (if (<= y 9e-23)
           (/ x (exp (* a b)))
           (if (<= y 7.2e+282)
             t_1
             (+ x (* t (- (* t (* (* x 0.5) (* y y))) (* x y)))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * pow(z, y);
	double tmp;
	if (y <= -8.2e+174) {
		tmp = t_1;
	} else if (y <= -5.2e+76) {
		tmp = x / ((y * (t + (y * ((0.16666666666666666 * (y * (t * (t * t)))) + ((t * t) * 0.5))))) + 1.0);
	} else if (y <= -2500.0) {
		tmp = t_1;
	} else if (y <= 9e-23) {
		tmp = x / exp((a * b));
	} else if (y <= 7.2e+282) {
		tmp = t_1;
	} else {
		tmp = x + (t * ((t * ((x * 0.5) * (y * y))) - (x * y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (z ** y)
    if (y <= (-8.2d+174)) then
        tmp = t_1
    else if (y <= (-5.2d+76)) then
        tmp = x / ((y * (t + (y * ((0.16666666666666666d0 * (y * (t * (t * t)))) + ((t * t) * 0.5d0))))) + 1.0d0)
    else if (y <= (-2500.0d0)) then
        tmp = t_1
    else if (y <= 9d-23) then
        tmp = x / exp((a * b))
    else if (y <= 7.2d+282) then
        tmp = t_1
    else
        tmp = x + (t * ((t * ((x * 0.5d0) * (y * y))) - (x * y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * Math.pow(z, y);
	double tmp;
	if (y <= -8.2e+174) {
		tmp = t_1;
	} else if (y <= -5.2e+76) {
		tmp = x / ((y * (t + (y * ((0.16666666666666666 * (y * (t * (t * t)))) + ((t * t) * 0.5))))) + 1.0);
	} else if (y <= -2500.0) {
		tmp = t_1;
	} else if (y <= 9e-23) {
		tmp = x / Math.exp((a * b));
	} else if (y <= 7.2e+282) {
		tmp = t_1;
	} else {
		tmp = x + (t * ((t * ((x * 0.5) * (y * y))) - (x * y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * math.pow(z, y)
	tmp = 0
	if y <= -8.2e+174:
		tmp = t_1
	elif y <= -5.2e+76:
		tmp = x / ((y * (t + (y * ((0.16666666666666666 * (y * (t * (t * t)))) + ((t * t) * 0.5))))) + 1.0)
	elif y <= -2500.0:
		tmp = t_1
	elif y <= 9e-23:
		tmp = x / math.exp((a * b))
	elif y <= 7.2e+282:
		tmp = t_1
	else:
		tmp = x + (t * ((t * ((x * 0.5) * (y * y))) - (x * y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * (z ^ y))
	tmp = 0.0
	if (y <= -8.2e+174)
		tmp = t_1;
	elseif (y <= -5.2e+76)
		tmp = Float64(x / Float64(Float64(y * Float64(t + Float64(y * Float64(Float64(0.16666666666666666 * Float64(y * Float64(t * Float64(t * t)))) + Float64(Float64(t * t) * 0.5))))) + 1.0));
	elseif (y <= -2500.0)
		tmp = t_1;
	elseif (y <= 9e-23)
		tmp = Float64(x / exp(Float64(a * b)));
	elseif (y <= 7.2e+282)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(t * Float64(Float64(t * Float64(Float64(x * 0.5) * Float64(y * y))) - Float64(x * y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * (z ^ y);
	tmp = 0.0;
	if (y <= -8.2e+174)
		tmp = t_1;
	elseif (y <= -5.2e+76)
		tmp = x / ((y * (t + (y * ((0.16666666666666666 * (y * (t * (t * t)))) + ((t * t) * 0.5))))) + 1.0);
	elseif (y <= -2500.0)
		tmp = t_1;
	elseif (y <= 9e-23)
		tmp = x / exp((a * b));
	elseif (y <= 7.2e+282)
		tmp = t_1;
	else
		tmp = x + (t * ((t * ((x * 0.5) * (y * y))) - (x * y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8.2e+174], t$95$1, If[LessEqual[y, -5.2e+76], N[(x / N[(N[(y * N[(t + N[(y * N[(N[(0.16666666666666666 * N[(y * N[(t * N[(t * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t * t), $MachinePrecision] * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2500.0], t$95$1, If[LessEqual[y, 9e-23], N[(x / N[Exp[N[(a * b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.2e+282], t$95$1, N[(x + N[(t * N[(N[(t * N[(N[(x * 0.5), $MachinePrecision] * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -8.20000000000000061e174 or -5.1999999999999999e76 < y < -2500 or 8.9999999999999995e-23 < y < 7.19999999999999972e282

   1. Initial program 98.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 98.0%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in a around 0

      \[\leadsto \color{blue}{\frac{x}{e^{y \cdot \left(t - \log z\right)}}} \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(e^{y \cdot \left(t - \log z\right)}\right)}\right) \]

      2. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\left(y \cdot \left(t - \log z\right)\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, \left(t - \log z\right)\right)\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, \log z\right)\right)\right)\right) \]

      5. log-lowering-log.f64 88.8%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, \mathsf{log.f64}\left(z\right)\right)\right)\right)\right) \]

   7. Simplified 88.8%

      \[\leadsto \color{blue}{\frac{x}{e^{y \cdot \left(t - \log z\right)}}} \]

   8. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\frac{x}{e^{-1 \cdot \left(y \cdot \log z\right)}}} \]
   9. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(e^{-1 \cdot \left(y \cdot \log z\right)}\right)}\right) \]

      2. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(e^{\mathsf{neg}\left(y \cdot \log z\right)}\right)\right) \]

      3. exp-neg N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(\frac{1}{\color{blue}{e^{y \cdot \log z}}}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(1, \color{blue}{\left(e^{y \cdot \log z}\right)}\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(1, \left(e^{\log z \cdot y}\right)\right)\right) \]

      6. exp-to-pow N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(1, \left({z}^{\color{blue}{y}}\right)\right)\right) \]

      7. pow-lowering-pow.f64 72.6%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(1, \mathsf{pow.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

   10. Simplified 72.6%

       \[\leadsto \color{blue}{\frac{x}{\frac{1}{{z}^{y}}}} \]
   11. Step-by-step derivation

       1. associate-/r/ N/A

          \[\leadsto \frac{x}{1} \cdot \color{blue}{{z}^{y}} \]

       2. /-rgt-identity N/A

          \[\leadsto x \cdot {\color{blue}{z}}^{y} \]

       3. *-commutative N/A

          \[\leadsto {z}^{y} \cdot \color{blue}{x} \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left({z}^{y}\right), \color{blue}{x}\right) \]

       5. pow-lowering-pow.f64 72.6%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{pow.f64}\left(z, y\right), x\right) \]

   12. Applied egg-rr 72.6%

       \[\leadsto \color{blue}{{z}^{y} \cdot x} \]

   if -8.20000000000000061e174 < y < -5.1999999999999999e76

   1. Initial program 100.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(t \cdot y\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\left(y \cdot t\right)\right)\right) \]

      2. *-lowering-*.f64 82.8%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, t\right)\right)\right) \]

   7. Simplified 82.8%

      \[\leadsto \frac{x}{e^{\color{blue}{y \cdot t}}} \]

   8. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + y \cdot \left(t + y \cdot \left(\frac{1}{6} \cdot \left({t}^{3} \cdot y\right) + \frac{1}{2} \cdot {t}^{2}\right)\right)\right)}\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(y \cdot \left(t + y \cdot \left(\frac{1}{6} \cdot \left({t}^{3} \cdot y\right) + \frac{1}{2} \cdot {t}^{2}\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \color{blue}{\left(t + y \cdot \left(\frac{1}{6} \cdot \left({t}^{3} \cdot y\right) + \frac{1}{2} \cdot {t}^{2}\right)\right)}\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \color{blue}{\left(y \cdot \left(\frac{1}{6} \cdot \left({t}^{3} \cdot y\right) + \frac{1}{2} \cdot {t}^{2}\right)\right)}\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{1}{6} \cdot \left({t}^{3} \cdot y\right) + \frac{1}{2} \cdot {t}^{2}\right)}\right)\right)\right)\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\left(\frac{1}{6} \cdot \left({t}^{3} \cdot y\right)\right), \color{blue}{\left(\frac{1}{2} \cdot {t}^{2}\right)}\right)\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, \left({t}^{3} \cdot y\right)\right), \left(\color{blue}{\frac{1}{2}} \cdot {t}^{2}\right)\right)\right)\right)\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, \left(y \cdot {t}^{3}\right)\right), \left(\frac{1}{2} \cdot {t}^{2}\right)\right)\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, \mathsf{*.f64}\left(y, \left({t}^{3}\right)\right)\right), \left(\frac{1}{2} \cdot {t}^{2}\right)\right)\right)\right)\right)\right)\right) \]

      9. cube-mult N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, \mathsf{*.f64}\left(y, \left(t \cdot \left(t \cdot t\right)\right)\right)\right), \left(\frac{1}{2} \cdot {t}^{2}\right)\right)\right)\right)\right)\right)\right) \]

      10. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, \mathsf{*.f64}\left(y, \left(t \cdot {t}^{2}\right)\right)\right), \left(\frac{1}{2} \cdot {t}^{2}\right)\right)\right)\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \left({t}^{2}\right)\right)\right)\right), \left(\frac{1}{2} \cdot {t}^{2}\right)\right)\right)\right)\right)\right)\right) \]

      12. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \left(t \cdot t\right)\right)\right)\right), \left(\frac{1}{2} \cdot {t}^{2}\right)\right)\right)\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(t, t\right)\right)\right)\right), \left(\frac{1}{2} \cdot {t}^{2}\right)\right)\right)\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(t, t\right)\right)\right)\right), \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{\left({t}^{2}\right)}\right)\right)\right)\right)\right)\right)\right) \]

      15. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(t, t\right)\right)\right)\right), \mathsf{*.f64}\left(\frac{1}{2}, \left(t \cdot \color{blue}{t}\right)\right)\right)\right)\right)\right)\right)\right) \]

      16. *-lowering-*.f64 77.3%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(t, t\right)\right)\right)\right), \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(t, \color{blue}{t}\right)\right)\right)\right)\right)\right)\right)\right) \]

   10. Simplified 77.3%

       \[\leadsto \frac{x}{\color{blue}{1 + y \cdot \left(t + y \cdot \left(0.16666666666666666 \cdot \left(y \cdot \left(t \cdot \left(t \cdot t\right)\right)\right) + 0.5 \cdot \left(t \cdot t\right)\right)\right)}} \]

   if -2500 < y < 8.9999999999999995e-23

   1. Initial program 94.2%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 94.2%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(a \cdot b\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 75.6%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, b\right)\right)\right) \]

   7. Simplified 75.6%

      \[\leadsto \frac{x}{e^{\color{blue}{a \cdot b}}} \]

   if 7.19999999999999972e282 < y

   1. Initial program 100.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(t \cdot y\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\left(y \cdot t\right)\right)\right) \]

      2. *-lowering-*.f64 100.0%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, t\right)\right)\right) \]

   7. Simplified 100.0%

      \[\leadsto \frac{x}{e^{\color{blue}{y \cdot t}}} \]

   8. Taylor expanded in t around 0

      \[\leadsto \color{blue}{x + t \cdot \left(-1 \cdot \left(t \cdot \left(-1 \cdot \left(x \cdot {y}^{2}\right) + \frac{1}{2} \cdot \left(x \cdot {y}^{2}\right)\right)\right) - x \cdot y\right)} \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(t \cdot \left(-1 \cdot \left(t \cdot \left(-1 \cdot \left(x \cdot {y}^{2}\right) + \frac{1}{2} \cdot \left(x \cdot {y}^{2}\right)\right)\right) - x \cdot y\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(t, \color{blue}{\left(-1 \cdot \left(t \cdot \left(-1 \cdot \left(x \cdot {y}^{2}\right) + \frac{1}{2} \cdot \left(x \cdot {y}^{2}\right)\right)\right) - x \cdot y\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(-1 \cdot \left(t \cdot \left(-1 \cdot \left(x \cdot {y}^{2}\right) + \frac{1}{2} \cdot \left(x \cdot {y}^{2}\right)\right)\right)\right), \color{blue}{\left(x \cdot y\right)}\right)\right)\right) \]

   10. Simplified 100.0%

       \[\leadsto \color{blue}{x + t \cdot \left(t \cdot \left(\left(0.5 \cdot x\right) \cdot \left(y \cdot y\right)\right) - x \cdot y\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+174}:\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{+76}:\\ \;\;\;\;\frac{x}{y \cdot \left(t + y \cdot \left(0.16666666666666666 \cdot \left(y \cdot \left(t \cdot \left(t \cdot t\right)\right)\right) + \left(t \cdot t\right) \cdot 0.5\right)\right) + 1}\\ \mathbf{elif}\;y \leq -2500:\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-23}:\\ \;\;\;\;\frac{x}{e^{a \cdot b}}\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+282}:\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \left(t \cdot \left(\left(x \cdot 0.5\right) \cdot \left(y \cdot y\right)\right) - x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 72.6% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{e^{a \cdot b}}\\ t_2 := \frac{x}{e^{y \cdot t}}\\ \mathbf{if}\;t \leq -4800:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -4.8 \cdot 10^{-206}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{-57}:\\ \;\;\;\;\frac{x}{\frac{1}{{z}^{y}}}\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{+77}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (exp (* a b)))) (t_2 (/ x (exp (* y t)))))
   (if (<= t -4800.0)
     t_2
     (if (<= t -4.8e-206)
       t_1
       (if (<= t 1.55e-57)
         (/ x (/ 1.0 (pow z y)))
         (if (<= t 1.55e+77) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / exp((a * b));
	double t_2 = x / exp((y * t));
	double tmp;
	if (t <= -4800.0) {
		tmp = t_2;
	} else if (t <= -4.8e-206) {
		tmp = t_1;
	} else if (t <= 1.55e-57) {
		tmp = x / (1.0 / pow(z, y));
	} else if (t <= 1.55e+77) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x / exp((a * b))
    t_2 = x / exp((y * t))
    if (t <= (-4800.0d0)) then
        tmp = t_2
    else if (t <= (-4.8d-206)) then
        tmp = t_1
    else if (t <= 1.55d-57) then
        tmp = x / (1.0d0 / (z ** y))
    else if (t <= 1.55d+77) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / Math.exp((a * b));
	double t_2 = x / Math.exp((y * t));
	double tmp;
	if (t <= -4800.0) {
		tmp = t_2;
	} else if (t <= -4.8e-206) {
		tmp = t_1;
	} else if (t <= 1.55e-57) {
		tmp = x / (1.0 / Math.pow(z, y));
	} else if (t <= 1.55e+77) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / math.exp((a * b))
	t_2 = x / math.exp((y * t))
	tmp = 0
	if t <= -4800.0:
		tmp = t_2
	elif t <= -4.8e-206:
		tmp = t_1
	elif t <= 1.55e-57:
		tmp = x / (1.0 / math.pow(z, y))
	elif t <= 1.55e+77:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / exp(Float64(a * b)))
	t_2 = Float64(x / exp(Float64(y * t)))
	tmp = 0.0
	if (t <= -4800.0)
		tmp = t_2;
	elseif (t <= -4.8e-206)
		tmp = t_1;
	elseif (t <= 1.55e-57)
		tmp = Float64(x / Float64(1.0 / (z ^ y)));
	elseif (t <= 1.55e+77)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / exp((a * b));
	t_2 = x / exp((y * t));
	tmp = 0.0;
	if (t <= -4800.0)
		tmp = t_2;
	elseif (t <= -4.8e-206)
		tmp = t_1;
	elseif (t <= 1.55e-57)
		tmp = x / (1.0 / (z ^ y));
	elseif (t <= 1.55e+77)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[Exp[N[(a * b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[Exp[N[(y * t), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4800.0], t$95$2, If[LessEqual[t, -4.8e-206], t$95$1, If[LessEqual[t, 1.55e-57], N[(x / N[(1.0 / N[Power[z, y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.55e+77], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4800 or 1.54999999999999999e77 < t

   1. Initial program 95.8%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 95.8%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(t \cdot y\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\left(y \cdot t\right)\right)\right) \]

      2. *-lowering-*.f64 84.9%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, t\right)\right)\right) \]

   7. Simplified 84.9%

      \[\leadsto \frac{x}{e^{\color{blue}{y \cdot t}}} \]

   if -4800 < t < -4.7999999999999999e-206 or 1.54999999999999988e-57 < t < 1.54999999999999999e77

   1. Initial program 96.4%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 96.4%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(a \cdot b\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 75.0%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, b\right)\right)\right) \]

   7. Simplified 75.0%

      \[\leadsto \frac{x}{e^{\color{blue}{a \cdot b}}} \]

   if -4.7999999999999999e-206 < t < 1.54999999999999988e-57

   1. Initial program 96.6%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 96.7%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in a around 0

      \[\leadsto \color{blue}{\frac{x}{e^{y \cdot \left(t - \log z\right)}}} \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(e^{y \cdot \left(t - \log z\right)}\right)}\right) \]

      2. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\left(y \cdot \left(t - \log z\right)\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, \left(t - \log z\right)\right)\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, \log z\right)\right)\right)\right) \]

      5. log-lowering-log.f64 77.2%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, \mathsf{log.f64}\left(z\right)\right)\right)\right)\right) \]

   7. Simplified 77.2%

      \[\leadsto \color{blue}{\frac{x}{e^{y \cdot \left(t - \log z\right)}}} \]

   8. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\frac{x}{e^{-1 \cdot \left(y \cdot \log z\right)}}} \]
   9. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(e^{-1 \cdot \left(y \cdot \log z\right)}\right)}\right) \]

      2. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(e^{\mathsf{neg}\left(y \cdot \log z\right)}\right)\right) \]

      3. exp-neg N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(\frac{1}{\color{blue}{e^{y \cdot \log z}}}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(1, \color{blue}{\left(e^{y \cdot \log z}\right)}\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(1, \left(e^{\log z \cdot y}\right)\right)\right) \]

      6. exp-to-pow N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(1, \left({z}^{\color{blue}{y}}\right)\right)\right) \]

      7. pow-lowering-pow.f64 77.2%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(1, \mathsf{pow.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

   10. Simplified 77.2%

       \[\leadsto \color{blue}{\frac{x}{\frac{1}{{z}^{y}}}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 7: 72.6% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{e^{a \cdot b}}\\ t_2 := \frac{x}{e^{y \cdot t}}\\ \mathbf{if}\;t \leq -4600:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -5.6 \cdot 10^{-206}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.08 \cdot 10^{-52}:\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+77}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (exp (* a b)))) (t_2 (/ x (exp (* y t)))))
   (if (<= t -4600.0)
     t_2
     (if (<= t -5.6e-206)
       t_1
       (if (<= t 1.08e-52) (* x (pow z y)) (if (<= t 1.45e+77) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / exp((a * b));
	double t_2 = x / exp((y * t));
	double tmp;
	if (t <= -4600.0) {
		tmp = t_2;
	} else if (t <= -5.6e-206) {
		tmp = t_1;
	} else if (t <= 1.08e-52) {
		tmp = x * pow(z, y);
	} else if (t <= 1.45e+77) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x / exp((a * b))
    t_2 = x / exp((y * t))
    if (t <= (-4600.0d0)) then
        tmp = t_2
    else if (t <= (-5.6d-206)) then
        tmp = t_1
    else if (t <= 1.08d-52) then
        tmp = x * (z ** y)
    else if (t <= 1.45d+77) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / Math.exp((a * b));
	double t_2 = x / Math.exp((y * t));
	double tmp;
	if (t <= -4600.0) {
		tmp = t_2;
	} else if (t <= -5.6e-206) {
		tmp = t_1;
	} else if (t <= 1.08e-52) {
		tmp = x * Math.pow(z, y);
	} else if (t <= 1.45e+77) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / math.exp((a * b))
	t_2 = x / math.exp((y * t))
	tmp = 0
	if t <= -4600.0:
		tmp = t_2
	elif t <= -5.6e-206:
		tmp = t_1
	elif t <= 1.08e-52:
		tmp = x * math.pow(z, y)
	elif t <= 1.45e+77:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / exp(Float64(a * b)))
	t_2 = Float64(x / exp(Float64(y * t)))
	tmp = 0.0
	if (t <= -4600.0)
		tmp = t_2;
	elseif (t <= -5.6e-206)
		tmp = t_1;
	elseif (t <= 1.08e-52)
		tmp = Float64(x * (z ^ y));
	elseif (t <= 1.45e+77)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / exp((a * b));
	t_2 = x / exp((y * t));
	tmp = 0.0;
	if (t <= -4600.0)
		tmp = t_2;
	elseif (t <= -5.6e-206)
		tmp = t_1;
	elseif (t <= 1.08e-52)
		tmp = x * (z ^ y);
	elseif (t <= 1.45e+77)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[Exp[N[(a * b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[Exp[N[(y * t), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4600.0], t$95$2, If[LessEqual[t, -5.6e-206], t$95$1, If[LessEqual[t, 1.08e-52], N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.45e+77], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4600 or 1.4500000000000001e77 < t

   1. Initial program 95.8%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 95.8%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(t \cdot y\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\left(y \cdot t\right)\right)\right) \]

      2. *-lowering-*.f64 84.9%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, t\right)\right)\right) \]

   7. Simplified 84.9%

      \[\leadsto \frac{x}{e^{\color{blue}{y \cdot t}}} \]

   if -4600 < t < -5.6000000000000003e-206 or 1.08e-52 < t < 1.4500000000000001e77

   1. Initial program 96.4%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 96.4%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(a \cdot b\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 75.0%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, b\right)\right)\right) \]

   7. Simplified 75.0%

      \[\leadsto \frac{x}{e^{\color{blue}{a \cdot b}}} \]

   if -5.6000000000000003e-206 < t < 1.08e-52

   1. Initial program 96.6%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 96.7%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in a around 0

      \[\leadsto \color{blue}{\frac{x}{e^{y \cdot \left(t - \log z\right)}}} \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(e^{y \cdot \left(t - \log z\right)}\right)}\right) \]

      2. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\left(y \cdot \left(t - \log z\right)\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, \left(t - \log z\right)\right)\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, \log z\right)\right)\right)\right) \]

      5. log-lowering-log.f64 77.2%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, \mathsf{log.f64}\left(z\right)\right)\right)\right)\right) \]

   7. Simplified 77.2%

      \[\leadsto \color{blue}{\frac{x}{e^{y \cdot \left(t - \log z\right)}}} \]

   8. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\frac{x}{e^{-1 \cdot \left(y \cdot \log z\right)}}} \]
   9. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(e^{-1 \cdot \left(y \cdot \log z\right)}\right)}\right) \]

      2. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(e^{\mathsf{neg}\left(y \cdot \log z\right)}\right)\right) \]

      3. exp-neg N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(\frac{1}{\color{blue}{e^{y \cdot \log z}}}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(1, \color{blue}{\left(e^{y \cdot \log z}\right)}\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(1, \left(e^{\log z \cdot y}\right)\right)\right) \]

      6. exp-to-pow N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(1, \left({z}^{\color{blue}{y}}\right)\right)\right) \]

      7. pow-lowering-pow.f64 77.2%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(1, \mathsf{pow.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

   10. Simplified 77.2%

       \[\leadsto \color{blue}{\frac{x}{\frac{1}{{z}^{y}}}} \]
   11. Step-by-step derivation

       1. associate-/r/ N/A

          \[\leadsto \frac{x}{1} \cdot \color{blue}{{z}^{y}} \]

       2. /-rgt-identity N/A

          \[\leadsto x \cdot {\color{blue}{z}}^{y} \]

       3. *-commutative N/A

          \[\leadsto {z}^{y} \cdot \color{blue}{x} \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left({z}^{y}\right), \color{blue}{x}\right) \]

       5. pow-lowering-pow.f64 77.1%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{pow.f64}\left(z, y\right), x\right) \]

   12. Applied egg-rr 77.1%

       \[\leadsto \color{blue}{{z}^{y} \cdot x} \]
3. Recombined 3 regimes into one program.

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4600:\\ \;\;\;\;\frac{x}{e^{y \cdot t}}\\ \mathbf{elif}\;t \leq -5.6 \cdot 10^{-206}:\\ \;\;\;\;\frac{x}{e^{a \cdot b}}\\ \mathbf{elif}\;t \leq 1.08 \cdot 10^{-52}:\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+77}:\\ \;\;\;\;\frac{x}{e^{a \cdot b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{e^{y \cdot t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 47.4% accurate, 5.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + t \cdot \left(t \cdot \left(\left(x \cdot 0.5\right) \cdot \left(y \cdot y\right)\right) - x \cdot y\right)\\ t_2 := \left(t \cdot t\right) \cdot 0.5\\ t_3 := x \cdot t\_2\\ \mathbf{if}\;y \leq -8 \cdot 10^{+241}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -7 \cdot 10^{+70}:\\ \;\;\;\;\frac{x}{t \cdot \left(y + t \cdot \left(\left(t \cdot 0.16666666666666666\right) \cdot \left(y \cdot \left(y \cdot y\right)\right) + 0.5 \cdot \left(y \cdot y\right)\right)\right) + 1}\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-59}:\\ \;\;\;\;\frac{2 \cdot \frac{x}{a \cdot a}}{b \cdot b}\\ \mathbf{elif}\;y \leq -2.35 \cdot 10^{-200}:\\ \;\;\;\;\frac{x}{y \cdot \left(t + y \cdot \left(0.16666666666666666 \cdot \left(y \cdot \left(t \cdot \left(t \cdot t\right)\right)\right) + t\_2\right)\right) + 1}\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-133}:\\ \;\;\;\;x + b \cdot \left(b \cdot \left(x \cdot \left(0.5 \cdot \left(a \cdot a\right)\right)\right) - x \cdot a\right)\\ \mathbf{elif}\;y \leq 0.0142:\\ \;\;\;\;\left(y \cdot y\right) \cdot \left(t\_3 + \frac{\frac{x}{y} - x \cdot t}{y}\right)\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+144}:\\ \;\;\;\;\left(y \cdot y\right) \cdot t\_3\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+282}:\\ \;\;\;\;\frac{x}{t \cdot \left(y + \left(y \cdot y\right) \cdot \left(t \cdot 0.5\right)\right) + 1}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* t (- (* t (* (* x 0.5) (* y y))) (* x y)))))
        (t_2 (* (* t t) 0.5))
        (t_3 (* x t_2)))
   (if (<= y -8e+241)
     t_1
     (if (<= y -7e+70)
       (/
        x
        (+
         (*
          t
          (+
           y
           (*
            t
            (+ (* (* t 0.16666666666666666) (* y (* y y))) (* 0.5 (* y y))))))
         1.0))
       (if (<= y -1.35e-59)
         (/ (* 2.0 (/ x (* a a))) (* b b))
         (if (<= y -2.35e-200)
           (/
            x
            (+
             (*
              y
              (+ t (* y (+ (* 0.16666666666666666 (* y (* t (* t t)))) t_2))))
             1.0))
           (if (<= y 1.5e-133)
             (+ x (* b (- (* b (* x (* 0.5 (* a a)))) (* x a))))
             (if (<= y 0.0142)
               (* (* y y) (+ t_3 (/ (- (/ x y) (* x t)) y)))
               (if (<= y 1.8e+144)
                 (* (* y y) t_3)
                 (if (<= y 7.2e+282)
                   (/ x (+ (* t (+ y (* (* y y) (* t 0.5)))) 1.0))
                   t_1))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (t * ((t * ((x * 0.5) * (y * y))) - (x * y)));
	double t_2 = (t * t) * 0.5;
	double t_3 = x * t_2;
	double tmp;
	if (y <= -8e+241) {
		tmp = t_1;
	} else if (y <= -7e+70) {
		tmp = x / ((t * (y + (t * (((t * 0.16666666666666666) * (y * (y * y))) + (0.5 * (y * y)))))) + 1.0);
	} else if (y <= -1.35e-59) {
		tmp = (2.0 * (x / (a * a))) / (b * b);
	} else if (y <= -2.35e-200) {
		tmp = x / ((y * (t + (y * ((0.16666666666666666 * (y * (t * (t * t)))) + t_2)))) + 1.0);
	} else if (y <= 1.5e-133) {
		tmp = x + (b * ((b * (x * (0.5 * (a * a)))) - (x * a)));
	} else if (y <= 0.0142) {
		tmp = (y * y) * (t_3 + (((x / y) - (x * t)) / y));
	} else if (y <= 1.8e+144) {
		tmp = (y * y) * t_3;
	} else if (y <= 7.2e+282) {
		tmp = x / ((t * (y + ((y * y) * (t * 0.5)))) + 1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x + (t * ((t * ((x * 0.5d0) * (y * y))) - (x * y)))
    t_2 = (t * t) * 0.5d0
    t_3 = x * t_2
    if (y <= (-8d+241)) then
        tmp = t_1
    else if (y <= (-7d+70)) then
        tmp = x / ((t * (y + (t * (((t * 0.16666666666666666d0) * (y * (y * y))) + (0.5d0 * (y * y)))))) + 1.0d0)
    else if (y <= (-1.35d-59)) then
        tmp = (2.0d0 * (x / (a * a))) / (b * b)
    else if (y <= (-2.35d-200)) then
        tmp = x / ((y * (t + (y * ((0.16666666666666666d0 * (y * (t * (t * t)))) + t_2)))) + 1.0d0)
    else if (y <= 1.5d-133) then
        tmp = x + (b * ((b * (x * (0.5d0 * (a * a)))) - (x * a)))
    else if (y <= 0.0142d0) then
        tmp = (y * y) * (t_3 + (((x / y) - (x * t)) / y))
    else if (y <= 1.8d+144) then
        tmp = (y * y) * t_3
    else if (y <= 7.2d+282) then
        tmp = x / ((t * (y + ((y * y) * (t * 0.5d0)))) + 1.0d0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (t * ((t * ((x * 0.5) * (y * y))) - (x * y)));
	double t_2 = (t * t) * 0.5;
	double t_3 = x * t_2;
	double tmp;
	if (y <= -8e+241) {
		tmp = t_1;
	} else if (y <= -7e+70) {
		tmp = x / ((t * (y + (t * (((t * 0.16666666666666666) * (y * (y * y))) + (0.5 * (y * y)))))) + 1.0);
	} else if (y <= -1.35e-59) {
		tmp = (2.0 * (x / (a * a))) / (b * b);
	} else if (y <= -2.35e-200) {
		tmp = x / ((y * (t + (y * ((0.16666666666666666 * (y * (t * (t * t)))) + t_2)))) + 1.0);
	} else if (y <= 1.5e-133) {
		tmp = x + (b * ((b * (x * (0.5 * (a * a)))) - (x * a)));
	} else if (y <= 0.0142) {
		tmp = (y * y) * (t_3 + (((x / y) - (x * t)) / y));
	} else if (y <= 1.8e+144) {
		tmp = (y * y) * t_3;
	} else if (y <= 7.2e+282) {
		tmp = x / ((t * (y + ((y * y) * (t * 0.5)))) + 1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (t * ((t * ((x * 0.5) * (y * y))) - (x * y)))
	t_2 = (t * t) * 0.5
	t_3 = x * t_2
	tmp = 0
	if y <= -8e+241:
		tmp = t_1
	elif y <= -7e+70:
		tmp = x / ((t * (y + (t * (((t * 0.16666666666666666) * (y * (y * y))) + (0.5 * (y * y)))))) + 1.0)
	elif y <= -1.35e-59:
		tmp = (2.0 * (x / (a * a))) / (b * b)
	elif y <= -2.35e-200:
		tmp = x / ((y * (t + (y * ((0.16666666666666666 * (y * (t * (t * t)))) + t_2)))) + 1.0)
	elif y <= 1.5e-133:
		tmp = x + (b * ((b * (x * (0.5 * (a * a)))) - (x * a)))
	elif y <= 0.0142:
		tmp = (y * y) * (t_3 + (((x / y) - (x * t)) / y))
	elif y <= 1.8e+144:
		tmp = (y * y) * t_3
	elif y <= 7.2e+282:
		tmp = x / ((t * (y + ((y * y) * (t * 0.5)))) + 1.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(t * Float64(Float64(t * Float64(Float64(x * 0.5) * Float64(y * y))) - Float64(x * y))))
	t_2 = Float64(Float64(t * t) * 0.5)
	t_3 = Float64(x * t_2)
	tmp = 0.0
	if (y <= -8e+241)
		tmp = t_1;
	elseif (y <= -7e+70)
		tmp = Float64(x / Float64(Float64(t * Float64(y + Float64(t * Float64(Float64(Float64(t * 0.16666666666666666) * Float64(y * Float64(y * y))) + Float64(0.5 * Float64(y * y)))))) + 1.0));
	elseif (y <= -1.35e-59)
		tmp = Float64(Float64(2.0 * Float64(x / Float64(a * a))) / Float64(b * b));
	elseif (y <= -2.35e-200)
		tmp = Float64(x / Float64(Float64(y * Float64(t + Float64(y * Float64(Float64(0.16666666666666666 * Float64(y * Float64(t * Float64(t * t)))) + t_2)))) + 1.0));
	elseif (y <= 1.5e-133)
		tmp = Float64(x + Float64(b * Float64(Float64(b * Float64(x * Float64(0.5 * Float64(a * a)))) - Float64(x * a))));
	elseif (y <= 0.0142)
		tmp = Float64(Float64(y * y) * Float64(t_3 + Float64(Float64(Float64(x / y) - Float64(x * t)) / y)));
	elseif (y <= 1.8e+144)
		tmp = Float64(Float64(y * y) * t_3);
	elseif (y <= 7.2e+282)
		tmp = Float64(x / Float64(Float64(t * Float64(y + Float64(Float64(y * y) * Float64(t * 0.5)))) + 1.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (t * ((t * ((x * 0.5) * (y * y))) - (x * y)));
	t_2 = (t * t) * 0.5;
	t_3 = x * t_2;
	tmp = 0.0;
	if (y <= -8e+241)
		tmp = t_1;
	elseif (y <= -7e+70)
		tmp = x / ((t * (y + (t * (((t * 0.16666666666666666) * (y * (y * y))) + (0.5 * (y * y)))))) + 1.0);
	elseif (y <= -1.35e-59)
		tmp = (2.0 * (x / (a * a))) / (b * b);
	elseif (y <= -2.35e-200)
		tmp = x / ((y * (t + (y * ((0.16666666666666666 * (y * (t * (t * t)))) + t_2)))) + 1.0);
	elseif (y <= 1.5e-133)
		tmp = x + (b * ((b * (x * (0.5 * (a * a)))) - (x * a)));
	elseif (y <= 0.0142)
		tmp = (y * y) * (t_3 + (((x / y) - (x * t)) / y));
	elseif (y <= 1.8e+144)
		tmp = (y * y) * t_3;
	elseif (y <= 7.2e+282)
		tmp = x / ((t * (y + ((y * y) * (t * 0.5)))) + 1.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(t * N[(N[(t * N[(N[(x * 0.5), $MachinePrecision] * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * t), $MachinePrecision] * 0.5), $MachinePrecision]}, Block[{t$95$3 = N[(x * t$95$2), $MachinePrecision]}, If[LessEqual[y, -8e+241], t$95$1, If[LessEqual[y, -7e+70], N[(x / N[(N[(t * N[(y + N[(t * N[(N[(N[(t * 0.16666666666666666), $MachinePrecision] * N[(y * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(0.5 * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.35e-59], N[(N[(2.0 * N[(x / N[(a * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(b * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.35e-200], N[(x / N[(N[(y * N[(t + N[(y * N[(N[(0.16666666666666666 * N[(y * N[(t * N[(t * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.5e-133], N[(x + N[(b * N[(N[(b * N[(x * N[(0.5 * N[(a * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 0.0142], N[(N[(y * y), $MachinePrecision] * N[(t$95$3 + N[(N[(N[(x / y), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.8e+144], N[(N[(y * y), $MachinePrecision] * t$95$3), $MachinePrecision], If[LessEqual[y, 7.2e+282], N[(x / N[(N[(t * N[(y + N[(N[(y * y), $MachinePrecision] * N[(t * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if y < -8.0000000000000004e241 or 7.19999999999999972e282 < y

   1. Initial program 100.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(t \cdot y\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\left(y \cdot t\right)\right)\right) \]

      2. *-lowering-*.f64 61.7%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, t\right)\right)\right) \]

   7. Simplified 61.7%

      \[\leadsto \frac{x}{e^{\color{blue}{y \cdot t}}} \]

   8. Taylor expanded in t around 0

      \[\leadsto \color{blue}{x + t \cdot \left(-1 \cdot \left(t \cdot \left(-1 \cdot \left(x \cdot {y}^{2}\right) + \frac{1}{2} \cdot \left(x \cdot {y}^{2}\right)\right)\right) - x \cdot y\right)} \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(t \cdot \left(-1 \cdot \left(t \cdot \left(-1 \cdot \left(x \cdot {y}^{2}\right) + \frac{1}{2} \cdot \left(x \cdot {y}^{2}\right)\right)\right) - x \cdot y\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(t, \color{blue}{\left(-1 \cdot \left(t \cdot \left(-1 \cdot \left(x \cdot {y}^{2}\right) + \frac{1}{2} \cdot \left(x \cdot {y}^{2}\right)\right)\right) - x \cdot y\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(-1 \cdot \left(t \cdot \left(-1 \cdot \left(x \cdot {y}^{2}\right) + \frac{1}{2} \cdot \left(x \cdot {y}^{2}\right)\right)\right)\right), \color{blue}{\left(x \cdot y\right)}\right)\right)\right) \]

   10. Simplified 69.8%

       \[\leadsto \color{blue}{x + t \cdot \left(t \cdot \left(\left(0.5 \cdot x\right) \cdot \left(y \cdot y\right)\right) - x \cdot y\right)} \]

   if -8.0000000000000004e241 < y < -7.00000000000000005e70

   1. Initial program 100.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(t \cdot y\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\left(y \cdot t\right)\right)\right) \]

      2. *-lowering-*.f64 82.7%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, t\right)\right)\right) \]

   7. Simplified 82.7%

      \[\leadsto \frac{x}{e^{\color{blue}{y \cdot t}}} \]

   8. Taylor expanded in t around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + t \cdot \left(y + t \cdot \left(\frac{1}{6} \cdot \left(t \cdot {y}^{3}\right) + \frac{1}{2} \cdot {y}^{2}\right)\right)\right)}\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(t \cdot \left(y + t \cdot \left(\frac{1}{6} \cdot \left(t \cdot {y}^{3}\right) + \frac{1}{2} \cdot {y}^{2}\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \color{blue}{\left(y + t \cdot \left(\frac{1}{6} \cdot \left(t \cdot {y}^{3}\right) + \frac{1}{2} \cdot {y}^{2}\right)\right)}\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(y, \color{blue}{\left(t \cdot \left(\frac{1}{6} \cdot \left(t \cdot {y}^{3}\right) + \frac{1}{2} \cdot {y}^{2}\right)\right)}\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(t, \color{blue}{\left(\frac{1}{6} \cdot \left(t \cdot {y}^{3}\right) + \frac{1}{2} \cdot {y}^{2}\right)}\right)\right)\right)\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\frac{1}{6} \cdot \left(t \cdot {y}^{3}\right)\right), \color{blue}{\left(\frac{1}{2} \cdot {y}^{2}\right)}\right)\right)\right)\right)\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\frac{1}{6} \cdot t\right) \cdot {y}^{3}\right), \left(\color{blue}{\frac{1}{2}} \cdot {y}^{2}\right)\right)\right)\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\frac{1}{6} \cdot t\right), \left({y}^{3}\right)\right), \left(\color{blue}{\frac{1}{2}} \cdot {y}^{2}\right)\right)\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, t\right), \left({y}^{3}\right)\right), \left(\frac{1}{2} \cdot {y}^{2}\right)\right)\right)\right)\right)\right)\right) \]

      9. cube-mult N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, t\right), \left(y \cdot \left(y \cdot y\right)\right)\right), \left(\frac{1}{2} \cdot {y}^{2}\right)\right)\right)\right)\right)\right)\right) \]

      10. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, t\right), \left(y \cdot {y}^{2}\right)\right), \left(\frac{1}{2} \cdot {y}^{2}\right)\right)\right)\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, t\right), \mathsf{*.f64}\left(y, \left({y}^{2}\right)\right)\right), \left(\frac{1}{2} \cdot {y}^{2}\right)\right)\right)\right)\right)\right)\right) \]

      12. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, t\right), \mathsf{*.f64}\left(y, \left(y \cdot y\right)\right)\right), \left(\frac{1}{2} \cdot {y}^{2}\right)\right)\right)\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, t\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, y\right)\right)\right), \left(\frac{1}{2} \cdot {y}^{2}\right)\right)\right)\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, t\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, y\right)\right)\right), \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{\left({y}^{2}\right)}\right)\right)\right)\right)\right)\right)\right) \]

      15. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, t\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, y\right)\right)\right), \mathsf{*.f64}\left(\frac{1}{2}, \left(y \cdot \color{blue}{y}\right)\right)\right)\right)\right)\right)\right)\right) \]

      16. *-lowering-*.f64 64.7%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, t\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, y\right)\right)\right), \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(y, \color{blue}{y}\right)\right)\right)\right)\right)\right)\right)\right) \]

   10. Simplified 64.7%

       \[\leadsto \frac{x}{\color{blue}{1 + t \cdot \left(y + t \cdot \left(\left(0.16666666666666666 \cdot t\right) \cdot \left(y \cdot \left(y \cdot y\right)\right) + 0.5 \cdot \left(y \cdot y\right)\right)\right)}} \]

   if -7.00000000000000005e70 < y < -1.3499999999999999e-59

   1. Initial program 96.7%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 96.7%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(a \cdot b\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 44.3%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, b\right)\right)\right) \]

   7. Simplified 44.3%

      \[\leadsto \frac{x}{e^{\color{blue}{a \cdot b}}} \]

   8. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + b \cdot \left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)\right)}\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(b \cdot \left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \color{blue}{\left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \color{blue}{\left(\frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right)\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(\left(\frac{1}{2} \cdot {a}^{2}\right) \cdot \color{blue}{b}\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\left(\frac{1}{2} \cdot {a}^{2}\right), \color{blue}{b}\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left({a}^{2}\right)\right), b\right)\right)\right)\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left(a \cdot a\right)\right), b\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 24.8%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(a, a\right)\right), b\right)\right)\right)\right)\right) \]

   10. Simplified 24.8%

       \[\leadsto \frac{x}{\color{blue}{1 + b \cdot \left(a + \left(0.5 \cdot \left(a \cdot a\right)\right) \cdot b\right)}} \]
   11. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(b \cdot \color{blue}{\left(\frac{1}{2} \cdot \left(a \cdot a\right)\right)}\right)\right)\right)\right)\right) \]

       2. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(b \cdot \left(\left(\frac{1}{2} \cdot a\right) \cdot \color{blue}{a}\right)\right)\right)\right)\right)\right) \]

       3. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(\left(b \cdot \left(\frac{1}{2} \cdot a\right)\right) \cdot \color{blue}{a}\right)\right)\right)\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\left(b \cdot \left(\frac{1}{2} \cdot a\right)\right), \color{blue}{a}\right)\right)\right)\right)\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \left(\frac{1}{2} \cdot a\right)\right), a\right)\right)\right)\right)\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \left(a \cdot \frac{1}{2}\right)\right), a\right)\right)\right)\right)\right) \]

       7. *-lowering-*.f64 24.8%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \frac{1}{2}\right)\right), a\right)\right)\right)\right)\right) \]

   12. Applied egg-rr 24.8%

       \[\leadsto \frac{x}{1 + b \cdot \left(a + \color{blue}{\left(b \cdot \left(a \cdot 0.5\right)\right) \cdot a}\right)} \]

   13. Taylor expanded in b around inf

       \[\leadsto \color{blue}{2 \cdot \frac{x}{{a}^{2} \cdot {b}^{2}}} \]
   14. Step-by-step derivation

       1. associate-/r* N/A

          \[\leadsto 2 \cdot \frac{\frac{x}{{a}^{2}}}{\color{blue}{{b}^{2}}} \]

       2. associate-*r/ N/A

          \[\leadsto \frac{2 \cdot \frac{x}{{a}^{2}}}{\color{blue}{{b}^{2}}} \]

       3. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left(2 \cdot \frac{x}{{a}^{2}}\right), \color{blue}{\left({b}^{2}\right)}\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(2, \left(\frac{x}{{a}^{2}}\right)\right), \left({\color{blue}{b}}^{2}\right)\right) \]

       5. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(2, \mathsf{/.f64}\left(x, \left({a}^{2}\right)\right)\right), \left({b}^{2}\right)\right) \]

       6. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(2, \mathsf{/.f64}\left(x, \left(a \cdot a\right)\right)\right), \left({b}^{2}\right)\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(2, \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, a\right)\right)\right), \left({b}^{2}\right)\right) \]

       8. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(2, \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, a\right)\right)\right), \left(b \cdot \color{blue}{b}\right)\right) \]

       9. *-lowering-*.f64 54.3%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(2, \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, a\right)\right)\right), \mathsf{*.f64}\left(b, \color{blue}{b}\right)\right) \]

   15. Simplified 54.3%

       \[\leadsto \color{blue}{\frac{2 \cdot \frac{x}{a \cdot a}}{b \cdot b}} \]

   if -1.3499999999999999e-59 < y < -2.35e-200

   1. Initial program 91.1%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 91.1%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(t \cdot y\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\left(y \cdot t\right)\right)\right) \]

      2. *-lowering-*.f64 63.2%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, t\right)\right)\right) \]

   7. Simplified 63.2%

      \[\leadsto \frac{x}{e^{\color{blue}{y \cdot t}}} \]

   8. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + y \cdot \left(t + y \cdot \left(\frac{1}{6} \cdot \left({t}^{3} \cdot y\right) + \frac{1}{2} \cdot {t}^{2}\right)\right)\right)}\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(y \cdot \left(t + y \cdot \left(\frac{1}{6} \cdot \left({t}^{3} \cdot y\right) + \frac{1}{2} \cdot {t}^{2}\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \color{blue}{\left(t + y \cdot \left(\frac{1}{6} \cdot \left({t}^{3} \cdot y\right) + \frac{1}{2} \cdot {t}^{2}\right)\right)}\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \color{blue}{\left(y \cdot \left(\frac{1}{6} \cdot \left({t}^{3} \cdot y\right) + \frac{1}{2} \cdot {t}^{2}\right)\right)}\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{1}{6} \cdot \left({t}^{3} \cdot y\right) + \frac{1}{2} \cdot {t}^{2}\right)}\right)\right)\right)\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\left(\frac{1}{6} \cdot \left({t}^{3} \cdot y\right)\right), \color{blue}{\left(\frac{1}{2} \cdot {t}^{2}\right)}\right)\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, \left({t}^{3} \cdot y\right)\right), \left(\color{blue}{\frac{1}{2}} \cdot {t}^{2}\right)\right)\right)\right)\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, \left(y \cdot {t}^{3}\right)\right), \left(\frac{1}{2} \cdot {t}^{2}\right)\right)\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, \mathsf{*.f64}\left(y, \left({t}^{3}\right)\right)\right), \left(\frac{1}{2} \cdot {t}^{2}\right)\right)\right)\right)\right)\right)\right) \]

      9. cube-mult N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, \mathsf{*.f64}\left(y, \left(t \cdot \left(t \cdot t\right)\right)\right)\right), \left(\frac{1}{2} \cdot {t}^{2}\right)\right)\right)\right)\right)\right)\right) \]

      10. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, \mathsf{*.f64}\left(y, \left(t \cdot {t}^{2}\right)\right)\right), \left(\frac{1}{2} \cdot {t}^{2}\right)\right)\right)\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \left({t}^{2}\right)\right)\right)\right), \left(\frac{1}{2} \cdot {t}^{2}\right)\right)\right)\right)\right)\right)\right) \]

      12. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \left(t \cdot t\right)\right)\right)\right), \left(\frac{1}{2} \cdot {t}^{2}\right)\right)\right)\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(t, t\right)\right)\right)\right), \left(\frac{1}{2} \cdot {t}^{2}\right)\right)\right)\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(t, t\right)\right)\right)\right), \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{\left({t}^{2}\right)}\right)\right)\right)\right)\right)\right)\right) \]

      15. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(t, t\right)\right)\right)\right), \mathsf{*.f64}\left(\frac{1}{2}, \left(t \cdot \color{blue}{t}\right)\right)\right)\right)\right)\right)\right)\right) \]

      16. *-lowering-*.f64 62.9%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(t, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(t, t\right)\right)\right)\right), \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(t, \color{blue}{t}\right)\right)\right)\right)\right)\right)\right)\right) \]

   10. Simplified 62.9%

       \[\leadsto \frac{x}{\color{blue}{1 + y \cdot \left(t + y \cdot \left(0.16666666666666666 \cdot \left(y \cdot \left(t \cdot \left(t \cdot t\right)\right)\right) + 0.5 \cdot \left(t \cdot t\right)\right)\right)}} \]

   if -2.35e-200 < y < 1.5000000000000001e-133

   1. Initial program 94.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 94.0%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(a \cdot b\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 89.6%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, b\right)\right)\right) \]

   7. Simplified 89.6%

      \[\leadsto \frac{x}{e^{\color{blue}{a \cdot b}}} \]

   8. Taylor expanded in b around 0

      \[\leadsto \color{blue}{x + b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left({a}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({a}^{2} \cdot x\right)\right)\right) - a \cdot x\right)} \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left({a}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({a}^{2} \cdot x\right)\right)\right) - a \cdot x\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \color{blue}{\left(-1 \cdot \left(b \cdot \left(-1 \cdot \left({a}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({a}^{2} \cdot x\right)\right)\right) - a \cdot x\right)}\right)\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(\left(\mathsf{neg}\left(b \cdot \left(-1 \cdot \left({a}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({a}^{2} \cdot x\right)\right)\right)\right) - \color{blue}{a} \cdot x\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(b \cdot \left(\mathsf{neg}\left(\left(-1 \cdot \left({a}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({a}^{2} \cdot x\right)\right)\right)\right) - \color{blue}{a} \cdot x\right)\right)\right) \]

      5. distribute-rgt-out N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(b \cdot \left(\mathsf{neg}\left(\left({a}^{2} \cdot x\right) \cdot \left(-1 + \frac{1}{2}\right)\right)\right) - a \cdot x\right)\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(b \cdot \left(\mathsf{neg}\left(\left({a}^{2} \cdot x\right) \cdot \frac{-1}{2}\right)\right) - a \cdot x\right)\right)\right) \]

      7. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(b \cdot \left(\left({a}^{2} \cdot x\right) \cdot \left(\mathsf{neg}\left(\frac{-1}{2}\right)\right)\right) - a \cdot x\right)\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(b \cdot \left(\left({a}^{2} \cdot x\right) \cdot \frac{1}{2}\right) - a \cdot x\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(b \cdot \left(\frac{1}{2} \cdot \left({a}^{2} \cdot x\right)\right) - a \cdot x\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(b \cdot \left(\frac{1}{2} \cdot \left({a}^{2} \cdot x\right)\right)\right), \color{blue}{\left(a \cdot x\right)}\right)\right)\right) \]

   10. Simplified 67.1%

       \[\leadsto \color{blue}{x + b \cdot \left(b \cdot \left(\left(0.5 \cdot \left(a \cdot a\right)\right) \cdot x\right) - x \cdot a\right)} \]

   if 1.5000000000000001e-133 < y < 0.014200000000000001

   1. Initial program 96.3%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 96.4%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(t \cdot y\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\left(y \cdot t\right)\right)\right) \]

      2. *-lowering-*.f64 66.3%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, t\right)\right)\right) \]

   7. Simplified 66.3%

      \[\leadsto \frac{x}{e^{\color{blue}{y \cdot t}}} \]

   8. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x + y \cdot \left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) - t \cdot x\right)} \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot \left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) - t \cdot x\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) - t \cdot x\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right)\right), \color{blue}{\left(t \cdot x\right)}\right)\right)\right) \]

   10. Simplified 58.9%

       \[\leadsto \color{blue}{x + y \cdot \left(y \cdot \left(0.5 \cdot \left(x \cdot \left(t \cdot t\right)\right)\right) - x \cdot t\right)} \]

   11. Taylor expanded in y around -inf

       \[\leadsto \color{blue}{{y}^{2} \cdot \left(-1 \cdot \frac{-1 \cdot \frac{x}{y} + t \cdot x}{y} + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)} \]
   12. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left({y}^{2}\right), \color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{x}{y} + t \cdot x}{y} + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)}\right) \]

       2. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(y \cdot y\right), \left(\color{blue}{-1 \cdot \frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}} + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \left(\color{blue}{-1 \cdot \frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}} + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) \]

       4. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right) + \color{blue}{-1 \cdot \frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}}\right)\right) \]

       5. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right) + \left(\mathsf{neg}\left(\frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}\right)\right)\right)\right) \]

       6. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right) - \color{blue}{\frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}}\right)\right) \]

       7. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right), \color{blue}{\left(\frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}\right)}\right)\right) \]

       8. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\left(\left({t}^{2} \cdot x\right) \cdot \frac{1}{2}\right), \left(\frac{\color{blue}{-1 \cdot \frac{x}{y} + t \cdot x}}{y}\right)\right)\right) \]

       9. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\left(\left(x \cdot {t}^{2}\right) \cdot \frac{1}{2}\right), \left(\frac{\color{blue}{-1 \cdot \frac{x}{y}} + t \cdot x}{y}\right)\right)\right) \]

       10. associate-*l* N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\left(x \cdot \left({t}^{2} \cdot \frac{1}{2}\right)\right), \left(\frac{\color{blue}{-1 \cdot \frac{x}{y} + t \cdot x}}{y}\right)\right)\right) \]

       11. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \left({t}^{2} \cdot \frac{1}{2}\right)\right), \left(\frac{\color{blue}{-1 \cdot \frac{x}{y} + t \cdot x}}{y}\right)\right)\right) \]

       12. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\left({t}^{2}\right), \frac{1}{2}\right)\right), \left(\frac{-1 \cdot \frac{x}{y} + \color{blue}{t \cdot x}}{y}\right)\right)\right) \]

       13. unpow2 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\left(t \cdot t\right), \frac{1}{2}\right)\right), \left(\frac{-1 \cdot \frac{x}{y} + \color{blue}{t} \cdot x}{y}\right)\right)\right) \]

       14. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, t\right), \frac{1}{2}\right)\right), \left(\frac{-1 \cdot \frac{x}{y} + \color{blue}{t} \cdot x}{y}\right)\right)\right) \]

       15. /-lowering-/.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, t\right), \frac{1}{2}\right)\right), \mathsf{/.f64}\left(\left(-1 \cdot \frac{x}{y} + t \cdot x\right), \color{blue}{y}\right)\right)\right) \]

   13. Simplified 65.7%

       \[\leadsto \color{blue}{\left(y \cdot y\right) \cdot \left(x \cdot \left(\left(t \cdot t\right) \cdot 0.5\right) - \frac{x \cdot t - \frac{x}{y}}{y}\right)} \]

   if 0.014200000000000001 < y < 1.7999999999999999e144

   1. Initial program 96.7%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 96.7%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(t \cdot y\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\left(y \cdot t\right)\right)\right) \]

      2. *-lowering-*.f64 51.2%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, t\right)\right)\right) \]

   7. Simplified 51.2%

      \[\leadsto \frac{x}{e^{\color{blue}{y \cdot t}}} \]

   8. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x + y \cdot \left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) - t \cdot x\right)} \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot \left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) - t \cdot x\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) - t \cdot x\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right)\right), \color{blue}{\left(t \cdot x\right)}\right)\right)\right) \]

   10. Simplified 22.0%

       \[\leadsto \color{blue}{x + y \cdot \left(y \cdot \left(0.5 \cdot \left(x \cdot \left(t \cdot t\right)\right)\right) - x \cdot t\right)} \]

   11. Taylor expanded in y around -inf

       \[\leadsto \color{blue}{{y}^{2} \cdot \left(-1 \cdot \frac{-1 \cdot \frac{x}{y} + t \cdot x}{y} + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)} \]
   12. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left({y}^{2}\right), \color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{x}{y} + t \cdot x}{y} + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)}\right) \]

       2. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(y \cdot y\right), \left(\color{blue}{-1 \cdot \frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}} + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \left(\color{blue}{-1 \cdot \frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}} + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) \]

       4. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right) + \color{blue}{-1 \cdot \frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}}\right)\right) \]

       5. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right) + \left(\mathsf{neg}\left(\frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}\right)\right)\right)\right) \]

       6. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right) - \color{blue}{\frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}}\right)\right) \]

       7. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right), \color{blue}{\left(\frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}\right)}\right)\right) \]

       8. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\left(\left({t}^{2} \cdot x\right) \cdot \frac{1}{2}\right), \left(\frac{\color{blue}{-1 \cdot \frac{x}{y} + t \cdot x}}{y}\right)\right)\right) \]

       9. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\left(\left(x \cdot {t}^{2}\right) \cdot \frac{1}{2}\right), \left(\frac{\color{blue}{-1 \cdot \frac{x}{y}} + t \cdot x}{y}\right)\right)\right) \]

       10. associate-*l* N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\left(x \cdot \left({t}^{2} \cdot \frac{1}{2}\right)\right), \left(\frac{\color{blue}{-1 \cdot \frac{x}{y} + t \cdot x}}{y}\right)\right)\right) \]

       11. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \left({t}^{2} \cdot \frac{1}{2}\right)\right), \left(\frac{\color{blue}{-1 \cdot \frac{x}{y} + t \cdot x}}{y}\right)\right)\right) \]

       12. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\left({t}^{2}\right), \frac{1}{2}\right)\right), \left(\frac{-1 \cdot \frac{x}{y} + \color{blue}{t \cdot x}}{y}\right)\right)\right) \]

       13. unpow2 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\left(t \cdot t\right), \frac{1}{2}\right)\right), \left(\frac{-1 \cdot \frac{x}{y} + \color{blue}{t} \cdot x}{y}\right)\right)\right) \]

       14. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, t\right), \frac{1}{2}\right)\right), \left(\frac{-1 \cdot \frac{x}{y} + \color{blue}{t} \cdot x}{y}\right)\right)\right) \]

       15. /-lowering-/.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, t\right), \frac{1}{2}\right)\right), \mathsf{/.f64}\left(\left(-1 \cdot \frac{x}{y} + t \cdot x\right), \color{blue}{y}\right)\right)\right) \]

   13. Simplified 28.3%

       \[\leadsto \color{blue}{\left(y \cdot y\right) \cdot \left(x \cdot \left(\left(t \cdot t\right) \cdot 0.5\right) - \frac{x \cdot t - \frac{x}{y}}{y}\right)} \]

   14. Taylor expanded in t around inf

       \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \color{blue}{\left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)}\right) \]
   15. Step-by-step derivation

       1. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \left(\left(\frac{1}{2} \cdot {t}^{2}\right) \cdot \color{blue}{x}\right)\right) \]

       2. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \left(x \cdot \color{blue}{\left(\frac{1}{2} \cdot {t}^{2}\right)}\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{1}{2} \cdot {t}^{2}\right)}\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{\left({t}^{2}\right)}\right)\right)\right) \]

       5. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{2}, \left(t \cdot \color{blue}{t}\right)\right)\right)\right) \]

       6. *-lowering-*.f64 51.0%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(t, \color{blue}{t}\right)\right)\right)\right) \]

   16. Simplified 51.0%

       \[\leadsto \left(y \cdot y\right) \cdot \color{blue}{\left(x \cdot \left(0.5 \cdot \left(t \cdot t\right)\right)\right)} \]

   if 1.7999999999999999e144 < y < 7.19999999999999972e282

   1. Initial program 100.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(t \cdot y\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\left(y \cdot t\right)\right)\right) \]

      2. *-lowering-*.f64 56.4%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, t\right)\right)\right) \]

   7. Simplified 56.4%

      \[\leadsto \frac{x}{e^{\color{blue}{y \cdot t}}} \]

   8. Taylor expanded in t around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + t \cdot \left(y + \frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right)\right)}\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(t \cdot \left(y + \frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \color{blue}{\left(y + \frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right)}\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(y, \color{blue}{\left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right)}\right)\right)\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(y, \left(\left(\frac{1}{2} \cdot t\right) \cdot \color{blue}{{y}^{2}}\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(\left(\frac{1}{2} \cdot t\right), \color{blue}{\left({y}^{2}\right)}\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, t\right), \left({\color{blue}{y}}^{2}\right)\right)\right)\right)\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, t\right), \left(y \cdot \color{blue}{y}\right)\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 85.3%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, t\right), \mathsf{*.f64}\left(y, \color{blue}{y}\right)\right)\right)\right)\right)\right) \]

   10. Simplified 85.3%

       \[\leadsto \frac{x}{\color{blue}{1 + t \cdot \left(y + \left(0.5 \cdot t\right) \cdot \left(y \cdot y\right)\right)}} \]
3. Recombined 8 regimes into one program.

4. Final simplification 64.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+241}:\\ \;\;\;\;x + t \cdot \left(t \cdot \left(\left(x \cdot 0.5\right) \cdot \left(y \cdot y\right)\right) - x \cdot y\right)\\ \mathbf{elif}\;y \leq -7 \cdot 10^{+70}:\\ \;\;\;\;\frac{x}{t \cdot \left(y + t \cdot \left(\left(t \cdot 0.16666666666666666\right) \cdot \left(y \cdot \left(y \cdot y\right)\right) + 0.5 \cdot \left(y \cdot y\right)\right)\right) + 1}\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-59}:\\ \;\;\;\;\frac{2 \cdot \frac{x}{a \cdot a}}{b \cdot b}\\ \mathbf{elif}\;y \leq -2.35 \cdot 10^{-200}:\\ \;\;\;\;\frac{x}{y \cdot \left(t + y \cdot \left(0.16666666666666666 \cdot \left(y \cdot \left(t \cdot \left(t \cdot t\right)\right)\right) + \left(t \cdot t\right) \cdot 0.5\right)\right) + 1}\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-133}:\\ \;\;\;\;x + b \cdot \left(b \cdot \left(x \cdot \left(0.5 \cdot \left(a \cdot a\right)\right)\right) - x \cdot a\right)\\ \mathbf{elif}\;y \leq 0.0142:\\ \;\;\;\;\left(y \cdot y\right) \cdot \left(x \cdot \left(\left(t \cdot t\right) \cdot 0.5\right) + \frac{\frac{x}{y} - x \cdot t}{y}\right)\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+144}:\\ \;\;\;\;\left(y \cdot y\right) \cdot \left(x \cdot \left(\left(t \cdot t\right) \cdot 0.5\right)\right)\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+282}:\\ \;\;\;\;\frac{x}{t \cdot \left(y + \left(y \cdot y\right) \cdot \left(t \cdot 0.5\right)\right) + 1}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \left(t \cdot \left(\left(x \cdot 0.5\right) \cdot \left(y \cdot y\right)\right) - x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 48.3% accurate, 5.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.5 \cdot \left(a \cdot a\right)\\ t_2 := x + t \cdot \left(t \cdot \left(\left(x \cdot 0.5\right) \cdot \left(y \cdot y\right)\right) - x \cdot y\right)\\ t_3 := x \cdot \left(\left(t \cdot t\right) \cdot 0.5\right)\\ \mathbf{if}\;y \leq -8.5 \cdot 10^{+241}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{+68}:\\ \;\;\;\;\frac{x}{t \cdot \left(y + t \cdot \left(\left(t \cdot 0.16666666666666666\right) \cdot \left(y \cdot \left(y \cdot y\right)\right) + 0.5 \cdot \left(y \cdot y\right)\right)\right) + 1}\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-55}:\\ \;\;\;\;\frac{2 \cdot \frac{x}{a \cdot a}}{b \cdot b}\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{-200}:\\ \;\;\;\;\frac{x}{b \cdot \left(a + b \cdot \left(0.16666666666666666 \cdot \left(b \cdot \left(a \cdot \left(a \cdot a\right)\right)\right) + t\_1\right)\right) + 1}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-133}:\\ \;\;\;\;x + b \cdot \left(b \cdot \left(x \cdot t\_1\right) - x \cdot a\right)\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{-7}:\\ \;\;\;\;\left(y \cdot y\right) \cdot \left(t\_3 + \frac{\frac{x}{y} - x \cdot t}{y}\right)\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+146}:\\ \;\;\;\;\left(y \cdot y\right) \cdot t\_3\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+282}:\\ \;\;\;\;\frac{x}{t \cdot \left(y + \left(y \cdot y\right) \cdot \left(t \cdot 0.5\right)\right) + 1}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* 0.5 (* a a)))
        (t_2 (+ x (* t (- (* t (* (* x 0.5) (* y y))) (* x y)))))
        (t_3 (* x (* (* t t) 0.5))))
   (if (<= y -8.5e+241)
     t_2
     (if (<= y -2.2e+68)
       (/
        x
        (+
         (*
          t
          (+
           y
           (*
            t
            (+ (* (* t 0.16666666666666666) (* y (* y y))) (* 0.5 (* y y))))))
         1.0))
       (if (<= y -2.3e-55)
         (/ (* 2.0 (/ x (* a a))) (* b b))
         (if (<= y -1.25e-200)
           (/
            x
            (+
             (*
              b
              (+ a (* b (+ (* 0.16666666666666666 (* b (* a (* a a)))) t_1))))
             1.0))
           (if (<= y 1.6e-133)
             (+ x (* b (- (* b (* x t_1)) (* x a))))
             (if (<= y 8.8e-7)
               (* (* y y) (+ t_3 (/ (- (/ x y) (* x t)) y)))
               (if (<= y 3e+146)
                 (* (* y y) t_3)
                 (if (<= y 7.2e+282)
                   (/ x (+ (* t (+ y (* (* y y) (* t 0.5)))) 1.0))
                   t_2))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 0.5 * (a * a);
	double t_2 = x + (t * ((t * ((x * 0.5) * (y * y))) - (x * y)));
	double t_3 = x * ((t * t) * 0.5);
	double tmp;
	if (y <= -8.5e+241) {
		tmp = t_2;
	} else if (y <= -2.2e+68) {
		tmp = x / ((t * (y + (t * (((t * 0.16666666666666666) * (y * (y * y))) + (0.5 * (y * y)))))) + 1.0);
	} else if (y <= -2.3e-55) {
		tmp = (2.0 * (x / (a * a))) / (b * b);
	} else if (y <= -1.25e-200) {
		tmp = x / ((b * (a + (b * ((0.16666666666666666 * (b * (a * (a * a)))) + t_1)))) + 1.0);
	} else if (y <= 1.6e-133) {
		tmp = x + (b * ((b * (x * t_1)) - (x * a)));
	} else if (y <= 8.8e-7) {
		tmp = (y * y) * (t_3 + (((x / y) - (x * t)) / y));
	} else if (y <= 3e+146) {
		tmp = (y * y) * t_3;
	} else if (y <= 7.2e+282) {
		tmp = x / ((t * (y + ((y * y) * (t * 0.5)))) + 1.0);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = 0.5d0 * (a * a)
    t_2 = x + (t * ((t * ((x * 0.5d0) * (y * y))) - (x * y)))
    t_3 = x * ((t * t) * 0.5d0)
    if (y <= (-8.5d+241)) then
        tmp = t_2
    else if (y <= (-2.2d+68)) then
        tmp = x / ((t * (y + (t * (((t * 0.16666666666666666d0) * (y * (y * y))) + (0.5d0 * (y * y)))))) + 1.0d0)
    else if (y <= (-2.3d-55)) then
        tmp = (2.0d0 * (x / (a * a))) / (b * b)
    else if (y <= (-1.25d-200)) then
        tmp = x / ((b * (a + (b * ((0.16666666666666666d0 * (b * (a * (a * a)))) + t_1)))) + 1.0d0)
    else if (y <= 1.6d-133) then
        tmp = x + (b * ((b * (x * t_1)) - (x * a)))
    else if (y <= 8.8d-7) then
        tmp = (y * y) * (t_3 + (((x / y) - (x * t)) / y))
    else if (y <= 3d+146) then
        tmp = (y * y) * t_3
    else if (y <= 7.2d+282) then
        tmp = x / ((t * (y + ((y * y) * (t * 0.5d0)))) + 1.0d0)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 0.5 * (a * a);
	double t_2 = x + (t * ((t * ((x * 0.5) * (y * y))) - (x * y)));
	double t_3 = x * ((t * t) * 0.5);
	double tmp;
	if (y <= -8.5e+241) {
		tmp = t_2;
	} else if (y <= -2.2e+68) {
		tmp = x / ((t * (y + (t * (((t * 0.16666666666666666) * (y * (y * y))) + (0.5 * (y * y)))))) + 1.0);
	} else if (y <= -2.3e-55) {
		tmp = (2.0 * (x / (a * a))) / (b * b);
	} else if (y <= -1.25e-200) {
		tmp = x / ((b * (a + (b * ((0.16666666666666666 * (b * (a * (a * a)))) + t_1)))) + 1.0);
	} else if (y <= 1.6e-133) {
		tmp = x + (b * ((b * (x * t_1)) - (x * a)));
	} else if (y <= 8.8e-7) {
		tmp = (y * y) * (t_3 + (((x / y) - (x * t)) / y));
	} else if (y <= 3e+146) {
		tmp = (y * y) * t_3;
	} else if (y <= 7.2e+282) {
		tmp = x / ((t * (y + ((y * y) * (t * 0.5)))) + 1.0);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = 0.5 * (a * a)
	t_2 = x + (t * ((t * ((x * 0.5) * (y * y))) - (x * y)))
	t_3 = x * ((t * t) * 0.5)
	tmp = 0
	if y <= -8.5e+241:
		tmp = t_2
	elif y <= -2.2e+68:
		tmp = x / ((t * (y + (t * (((t * 0.16666666666666666) * (y * (y * y))) + (0.5 * (y * y)))))) + 1.0)
	elif y <= -2.3e-55:
		tmp = (2.0 * (x / (a * a))) / (b * b)
	elif y <= -1.25e-200:
		tmp = x / ((b * (a + (b * ((0.16666666666666666 * (b * (a * (a * a)))) + t_1)))) + 1.0)
	elif y <= 1.6e-133:
		tmp = x + (b * ((b * (x * t_1)) - (x * a)))
	elif y <= 8.8e-7:
		tmp = (y * y) * (t_3 + (((x / y) - (x * t)) / y))
	elif y <= 3e+146:
		tmp = (y * y) * t_3
	elif y <= 7.2e+282:
		tmp = x / ((t * (y + ((y * y) * (t * 0.5)))) + 1.0)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(0.5 * Float64(a * a))
	t_2 = Float64(x + Float64(t * Float64(Float64(t * Float64(Float64(x * 0.5) * Float64(y * y))) - Float64(x * y))))
	t_3 = Float64(x * Float64(Float64(t * t) * 0.5))
	tmp = 0.0
	if (y <= -8.5e+241)
		tmp = t_2;
	elseif (y <= -2.2e+68)
		tmp = Float64(x / Float64(Float64(t * Float64(y + Float64(t * Float64(Float64(Float64(t * 0.16666666666666666) * Float64(y * Float64(y * y))) + Float64(0.5 * Float64(y * y)))))) + 1.0));
	elseif (y <= -2.3e-55)
		tmp = Float64(Float64(2.0 * Float64(x / Float64(a * a))) / Float64(b * b));
	elseif (y <= -1.25e-200)
		tmp = Float64(x / Float64(Float64(b * Float64(a + Float64(b * Float64(Float64(0.16666666666666666 * Float64(b * Float64(a * Float64(a * a)))) + t_1)))) + 1.0));
	elseif (y <= 1.6e-133)
		tmp = Float64(x + Float64(b * Float64(Float64(b * Float64(x * t_1)) - Float64(x * a))));
	elseif (y <= 8.8e-7)
		tmp = Float64(Float64(y * y) * Float64(t_3 + Float64(Float64(Float64(x / y) - Float64(x * t)) / y)));
	elseif (y <= 3e+146)
		tmp = Float64(Float64(y * y) * t_3);
	elseif (y <= 7.2e+282)
		tmp = Float64(x / Float64(Float64(t * Float64(y + Float64(Float64(y * y) * Float64(t * 0.5)))) + 1.0));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 0.5 * (a * a);
	t_2 = x + (t * ((t * ((x * 0.5) * (y * y))) - (x * y)));
	t_3 = x * ((t * t) * 0.5);
	tmp = 0.0;
	if (y <= -8.5e+241)
		tmp = t_2;
	elseif (y <= -2.2e+68)
		tmp = x / ((t * (y + (t * (((t * 0.16666666666666666) * (y * (y * y))) + (0.5 * (y * y)))))) + 1.0);
	elseif (y <= -2.3e-55)
		tmp = (2.0 * (x / (a * a))) / (b * b);
	elseif (y <= -1.25e-200)
		tmp = x / ((b * (a + (b * ((0.16666666666666666 * (b * (a * (a * a)))) + t_1)))) + 1.0);
	elseif (y <= 1.6e-133)
		tmp = x + (b * ((b * (x * t_1)) - (x * a)));
	elseif (y <= 8.8e-7)
		tmp = (y * y) * (t_3 + (((x / y) - (x * t)) / y));
	elseif (y <= 3e+146)
		tmp = (y * y) * t_3;
	elseif (y <= 7.2e+282)
		tmp = x / ((t * (y + ((y * y) * (t * 0.5)))) + 1.0);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(0.5 * N[(a * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(t * N[(N[(t * N[(N[(x * 0.5), $MachinePrecision] * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(N[(t * t), $MachinePrecision] * 0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8.5e+241], t$95$2, If[LessEqual[y, -2.2e+68], N[(x / N[(N[(t * N[(y + N[(t * N[(N[(N[(t * 0.16666666666666666), $MachinePrecision] * N[(y * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(0.5 * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.3e-55], N[(N[(2.0 * N[(x / N[(a * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(b * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.25e-200], N[(x / N[(N[(b * N[(a + N[(b * N[(N[(0.16666666666666666 * N[(b * N[(a * N[(a * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.6e-133], N[(x + N[(b * N[(N[(b * N[(x * t$95$1), $MachinePrecision]), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.8e-7], N[(N[(y * y), $MachinePrecision] * N[(t$95$3 + N[(N[(N[(x / y), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3e+146], N[(N[(y * y), $MachinePrecision] * t$95$3), $MachinePrecision], If[LessEqual[y, 7.2e+282], N[(x / N[(N[(t * N[(y + N[(N[(y * y), $MachinePrecision] * N[(t * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if y < -8.49999999999999954e241 or 7.19999999999999972e282 < y

   1. Initial program 100.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(t \cdot y\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\left(y \cdot t\right)\right)\right) \]

      2. *-lowering-*.f64 61.7%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, t\right)\right)\right) \]

   7. Simplified 61.7%

      \[\leadsto \frac{x}{e^{\color{blue}{y \cdot t}}} \]

   8. Taylor expanded in t around 0

      \[\leadsto \color{blue}{x + t \cdot \left(-1 \cdot \left(t \cdot \left(-1 \cdot \left(x \cdot {y}^{2}\right) + \frac{1}{2} \cdot \left(x \cdot {y}^{2}\right)\right)\right) - x \cdot y\right)} \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(t \cdot \left(-1 \cdot \left(t \cdot \left(-1 \cdot \left(x \cdot {y}^{2}\right) + \frac{1}{2} \cdot \left(x \cdot {y}^{2}\right)\right)\right) - x \cdot y\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(t, \color{blue}{\left(-1 \cdot \left(t \cdot \left(-1 \cdot \left(x \cdot {y}^{2}\right) + \frac{1}{2} \cdot \left(x \cdot {y}^{2}\right)\right)\right) - x \cdot y\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(-1 \cdot \left(t \cdot \left(-1 \cdot \left(x \cdot {y}^{2}\right) + \frac{1}{2} \cdot \left(x \cdot {y}^{2}\right)\right)\right)\right), \color{blue}{\left(x \cdot y\right)}\right)\right)\right) \]

   10. Simplified 69.8%

       \[\leadsto \color{blue}{x + t \cdot \left(t \cdot \left(\left(0.5 \cdot x\right) \cdot \left(y \cdot y\right)\right) - x \cdot y\right)} \]

   if -8.49999999999999954e241 < y < -2.19999999999999987e68

   1. Initial program 100.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(t \cdot y\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\left(y \cdot t\right)\right)\right) \]

      2. *-lowering-*.f64 82.7%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, t\right)\right)\right) \]

   7. Simplified 82.7%

      \[\leadsto \frac{x}{e^{\color{blue}{y \cdot t}}} \]

   8. Taylor expanded in t around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + t \cdot \left(y + t \cdot \left(\frac{1}{6} \cdot \left(t \cdot {y}^{3}\right) + \frac{1}{2} \cdot {y}^{2}\right)\right)\right)}\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(t \cdot \left(y + t \cdot \left(\frac{1}{6} \cdot \left(t \cdot {y}^{3}\right) + \frac{1}{2} \cdot {y}^{2}\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \color{blue}{\left(y + t \cdot \left(\frac{1}{6} \cdot \left(t \cdot {y}^{3}\right) + \frac{1}{2} \cdot {y}^{2}\right)\right)}\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(y, \color{blue}{\left(t \cdot \left(\frac{1}{6} \cdot \left(t \cdot {y}^{3}\right) + \frac{1}{2} \cdot {y}^{2}\right)\right)}\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(t, \color{blue}{\left(\frac{1}{6} \cdot \left(t \cdot {y}^{3}\right) + \frac{1}{2} \cdot {y}^{2}\right)}\right)\right)\right)\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\frac{1}{6} \cdot \left(t \cdot {y}^{3}\right)\right), \color{blue}{\left(\frac{1}{2} \cdot {y}^{2}\right)}\right)\right)\right)\right)\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\left(\left(\frac{1}{6} \cdot t\right) \cdot {y}^{3}\right), \left(\color{blue}{\frac{1}{2}} \cdot {y}^{2}\right)\right)\right)\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\frac{1}{6} \cdot t\right), \left({y}^{3}\right)\right), \left(\color{blue}{\frac{1}{2}} \cdot {y}^{2}\right)\right)\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, t\right), \left({y}^{3}\right)\right), \left(\frac{1}{2} \cdot {y}^{2}\right)\right)\right)\right)\right)\right)\right) \]

      9. cube-mult N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, t\right), \left(y \cdot \left(y \cdot y\right)\right)\right), \left(\frac{1}{2} \cdot {y}^{2}\right)\right)\right)\right)\right)\right)\right) \]

      10. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, t\right), \left(y \cdot {y}^{2}\right)\right), \left(\frac{1}{2} \cdot {y}^{2}\right)\right)\right)\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, t\right), \mathsf{*.f64}\left(y, \left({y}^{2}\right)\right)\right), \left(\frac{1}{2} \cdot {y}^{2}\right)\right)\right)\right)\right)\right)\right) \]

      12. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, t\right), \mathsf{*.f64}\left(y, \left(y \cdot y\right)\right)\right), \left(\frac{1}{2} \cdot {y}^{2}\right)\right)\right)\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, t\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, y\right)\right)\right), \left(\frac{1}{2} \cdot {y}^{2}\right)\right)\right)\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, t\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, y\right)\right)\right), \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{\left({y}^{2}\right)}\right)\right)\right)\right)\right)\right)\right) \]

      15. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, t\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, y\right)\right)\right), \mathsf{*.f64}\left(\frac{1}{2}, \left(y \cdot \color{blue}{y}\right)\right)\right)\right)\right)\right)\right)\right) \]

      16. *-lowering-*.f64 64.7%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, t\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, y\right)\right)\right), \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(y, \color{blue}{y}\right)\right)\right)\right)\right)\right)\right)\right) \]

   10. Simplified 64.7%

       \[\leadsto \frac{x}{\color{blue}{1 + t \cdot \left(y + t \cdot \left(\left(0.16666666666666666 \cdot t\right) \cdot \left(y \cdot \left(y \cdot y\right)\right) + 0.5 \cdot \left(y \cdot y\right)\right)\right)}} \]

   if -2.19999999999999987e68 < y < -2.30000000000000011e-55

   1. Initial program 96.6%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 96.6%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(a \cdot b\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 42.4%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, b\right)\right)\right) \]

   7. Simplified 42.4%

      \[\leadsto \frac{x}{e^{\color{blue}{a \cdot b}}} \]

   8. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + b \cdot \left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)\right)}\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(b \cdot \left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \color{blue}{\left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \color{blue}{\left(\frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right)\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(\left(\frac{1}{2} \cdot {a}^{2}\right) \cdot \color{blue}{b}\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\left(\frac{1}{2} \cdot {a}^{2}\right), \color{blue}{b}\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left({a}^{2}\right)\right), b\right)\right)\right)\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left(a \cdot a\right)\right), b\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 22.2%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(a, a\right)\right), b\right)\right)\right)\right)\right) \]

   10. Simplified 22.2%

       \[\leadsto \frac{x}{\color{blue}{1 + b \cdot \left(a + \left(0.5 \cdot \left(a \cdot a\right)\right) \cdot b\right)}} \]
   11. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(b \cdot \color{blue}{\left(\frac{1}{2} \cdot \left(a \cdot a\right)\right)}\right)\right)\right)\right)\right) \]

       2. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(b \cdot \left(\left(\frac{1}{2} \cdot a\right) \cdot \color{blue}{a}\right)\right)\right)\right)\right)\right) \]

       3. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(\left(b \cdot \left(\frac{1}{2} \cdot a\right)\right) \cdot \color{blue}{a}\right)\right)\right)\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\left(b \cdot \left(\frac{1}{2} \cdot a\right)\right), \color{blue}{a}\right)\right)\right)\right)\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \left(\frac{1}{2} \cdot a\right)\right), a\right)\right)\right)\right)\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \left(a \cdot \frac{1}{2}\right)\right), a\right)\right)\right)\right)\right) \]

       7. *-lowering-*.f64 22.2%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \frac{1}{2}\right)\right), a\right)\right)\right)\right)\right) \]

   12. Applied egg-rr 22.2%

       \[\leadsto \frac{x}{1 + b \cdot \left(a + \color{blue}{\left(b \cdot \left(a \cdot 0.5\right)\right) \cdot a}\right)} \]

   13. Taylor expanded in b around inf

       \[\leadsto \color{blue}{2 \cdot \frac{x}{{a}^{2} \cdot {b}^{2}}} \]
   14. Step-by-step derivation

       1. associate-/r* N/A

          \[\leadsto 2 \cdot \frac{\frac{x}{{a}^{2}}}{\color{blue}{{b}^{2}}} \]

       2. associate-*r/ N/A

          \[\leadsto \frac{2 \cdot \frac{x}{{a}^{2}}}{\color{blue}{{b}^{2}}} \]

       3. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left(2 \cdot \frac{x}{{a}^{2}}\right), \color{blue}{\left({b}^{2}\right)}\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(2, \left(\frac{x}{{a}^{2}}\right)\right), \left({\color{blue}{b}}^{2}\right)\right) \]

       5. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(2, \mathsf{/.f64}\left(x, \left({a}^{2}\right)\right)\right), \left({b}^{2}\right)\right) \]

       6. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(2, \mathsf{/.f64}\left(x, \left(a \cdot a\right)\right)\right), \left({b}^{2}\right)\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(2, \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, a\right)\right)\right), \left({b}^{2}\right)\right) \]

       8. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(2, \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, a\right)\right)\right), \left(b \cdot \color{blue}{b}\right)\right) \]

       9. *-lowering-*.f64 52.7%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(2, \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, a\right)\right)\right), \mathsf{*.f64}\left(b, \color{blue}{b}\right)\right) \]

   15. Simplified 52.7%

       \[\leadsto \color{blue}{\frac{2 \cdot \frac{x}{a \cdot a}}{b \cdot b}} \]

   if -2.30000000000000011e-55 < y < -1.24999999999999998e-200

   1. Initial program 91.4%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 91.4%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(a \cdot b\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 71.8%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, b\right)\right)\right) \]

   7. Simplified 71.8%

      \[\leadsto \frac{x}{e^{\color{blue}{a \cdot b}}} \]

   8. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + b \cdot \left(a + b \cdot \left(\frac{1}{6} \cdot \left({a}^{3} \cdot b\right) + \frac{1}{2} \cdot {a}^{2}\right)\right)\right)}\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(b \cdot \left(a + b \cdot \left(\frac{1}{6} \cdot \left({a}^{3} \cdot b\right) + \frac{1}{2} \cdot {a}^{2}\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \color{blue}{\left(a + b \cdot \left(\frac{1}{6} \cdot \left({a}^{3} \cdot b\right) + \frac{1}{2} \cdot {a}^{2}\right)\right)}\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \color{blue}{\left(b \cdot \left(\frac{1}{6} \cdot \left({a}^{3} \cdot b\right) + \frac{1}{2} \cdot {a}^{2}\right)\right)}\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \color{blue}{\left(\frac{1}{6} \cdot \left({a}^{3} \cdot b\right) + \frac{1}{2} \cdot {a}^{2}\right)}\right)\right)\right)\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\left(\frac{1}{6} \cdot \left({a}^{3} \cdot b\right)\right), \color{blue}{\left(\frac{1}{2} \cdot {a}^{2}\right)}\right)\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, \left({a}^{3} \cdot b\right)\right), \left(\color{blue}{\frac{1}{2}} \cdot {a}^{2}\right)\right)\right)\right)\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, \left(b \cdot {a}^{3}\right)\right), \left(\frac{1}{2} \cdot {a}^{2}\right)\right)\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, \mathsf{*.f64}\left(b, \left({a}^{3}\right)\right)\right), \left(\frac{1}{2} \cdot {a}^{2}\right)\right)\right)\right)\right)\right)\right) \]

      9. cube-mult N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, \mathsf{*.f64}\left(b, \left(a \cdot \left(a \cdot a\right)\right)\right)\right), \left(\frac{1}{2} \cdot {a}^{2}\right)\right)\right)\right)\right)\right)\right) \]

      10. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, \mathsf{*.f64}\left(b, \left(a \cdot {a}^{2}\right)\right)\right), \left(\frac{1}{2} \cdot {a}^{2}\right)\right)\right)\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \left({a}^{2}\right)\right)\right)\right), \left(\frac{1}{2} \cdot {a}^{2}\right)\right)\right)\right)\right)\right)\right) \]

      12. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \left(a \cdot a\right)\right)\right)\right), \left(\frac{1}{2} \cdot {a}^{2}\right)\right)\right)\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(a, a\right)\right)\right)\right), \left(\frac{1}{2} \cdot {a}^{2}\right)\right)\right)\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(a, a\right)\right)\right)\right), \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{\left({a}^{2}\right)}\right)\right)\right)\right)\right)\right)\right) \]

      15. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(a, a\right)\right)\right)\right), \mathsf{*.f64}\left(\frac{1}{2}, \left(a \cdot \color{blue}{a}\right)\right)\right)\right)\right)\right)\right)\right) \]

      16. *-lowering-*.f64 62.7%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(a, a\right)\right)\right)\right), \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(a, \color{blue}{a}\right)\right)\right)\right)\right)\right)\right)\right) \]

   10. Simplified 62.7%

       \[\leadsto \frac{x}{\color{blue}{1 + b \cdot \left(a + b \cdot \left(0.16666666666666666 \cdot \left(b \cdot \left(a \cdot \left(a \cdot a\right)\right)\right) + 0.5 \cdot \left(a \cdot a\right)\right)\right)}} \]

   if -1.24999999999999998e-200 < y < 1.60000000000000006e-133

   1. Initial program 94.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 94.0%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(a \cdot b\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 89.6%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, b\right)\right)\right) \]

   7. Simplified 89.6%

      \[\leadsto \frac{x}{e^{\color{blue}{a \cdot b}}} \]

   8. Taylor expanded in b around 0

      \[\leadsto \color{blue}{x + b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left({a}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({a}^{2} \cdot x\right)\right)\right) - a \cdot x\right)} \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left({a}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({a}^{2} \cdot x\right)\right)\right) - a \cdot x\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \color{blue}{\left(-1 \cdot \left(b \cdot \left(-1 \cdot \left({a}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({a}^{2} \cdot x\right)\right)\right) - a \cdot x\right)}\right)\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(\left(\mathsf{neg}\left(b \cdot \left(-1 \cdot \left({a}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({a}^{2} \cdot x\right)\right)\right)\right) - \color{blue}{a} \cdot x\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(b \cdot \left(\mathsf{neg}\left(\left(-1 \cdot \left({a}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({a}^{2} \cdot x\right)\right)\right)\right) - \color{blue}{a} \cdot x\right)\right)\right) \]

      5. distribute-rgt-out N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(b \cdot \left(\mathsf{neg}\left(\left({a}^{2} \cdot x\right) \cdot \left(-1 + \frac{1}{2}\right)\right)\right) - a \cdot x\right)\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(b \cdot \left(\mathsf{neg}\left(\left({a}^{2} \cdot x\right) \cdot \frac{-1}{2}\right)\right) - a \cdot x\right)\right)\right) \]

      7. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(b \cdot \left(\left({a}^{2} \cdot x\right) \cdot \left(\mathsf{neg}\left(\frac{-1}{2}\right)\right)\right) - a \cdot x\right)\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(b \cdot \left(\left({a}^{2} \cdot x\right) \cdot \frac{1}{2}\right) - a \cdot x\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(b \cdot \left(\frac{1}{2} \cdot \left({a}^{2} \cdot x\right)\right) - a \cdot x\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(b \cdot \left(\frac{1}{2} \cdot \left({a}^{2} \cdot x\right)\right)\right), \color{blue}{\left(a \cdot x\right)}\right)\right)\right) \]

   10. Simplified 67.1%

       \[\leadsto \color{blue}{x + b \cdot \left(b \cdot \left(\left(0.5 \cdot \left(a \cdot a\right)\right) \cdot x\right) - x \cdot a\right)} \]

   if 1.60000000000000006e-133 < y < 8.8000000000000004e-7

   1. Initial program 96.3%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 96.4%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(t \cdot y\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\left(y \cdot t\right)\right)\right) \]

      2. *-lowering-*.f64 66.3%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, t\right)\right)\right) \]

   7. Simplified 66.3%

      \[\leadsto \frac{x}{e^{\color{blue}{y \cdot t}}} \]

   8. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x + y \cdot \left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) - t \cdot x\right)} \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot \left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) - t \cdot x\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) - t \cdot x\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right)\right), \color{blue}{\left(t \cdot x\right)}\right)\right)\right) \]

   10. Simplified 58.9%

       \[\leadsto \color{blue}{x + y \cdot \left(y \cdot \left(0.5 \cdot \left(x \cdot \left(t \cdot t\right)\right)\right) - x \cdot t\right)} \]

   11. Taylor expanded in y around -inf

       \[\leadsto \color{blue}{{y}^{2} \cdot \left(-1 \cdot \frac{-1 \cdot \frac{x}{y} + t \cdot x}{y} + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)} \]
   12. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left({y}^{2}\right), \color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{x}{y} + t \cdot x}{y} + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)}\right) \]

       2. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(y \cdot y\right), \left(\color{blue}{-1 \cdot \frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}} + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \left(\color{blue}{-1 \cdot \frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}} + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) \]

       4. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right) + \color{blue}{-1 \cdot \frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}}\right)\right) \]

       5. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right) + \left(\mathsf{neg}\left(\frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}\right)\right)\right)\right) \]

       6. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right) - \color{blue}{\frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}}\right)\right) \]

       7. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right), \color{blue}{\left(\frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}\right)}\right)\right) \]

       8. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\left(\left({t}^{2} \cdot x\right) \cdot \frac{1}{2}\right), \left(\frac{\color{blue}{-1 \cdot \frac{x}{y} + t \cdot x}}{y}\right)\right)\right) \]

       9. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\left(\left(x \cdot {t}^{2}\right) \cdot \frac{1}{2}\right), \left(\frac{\color{blue}{-1 \cdot \frac{x}{y}} + t \cdot x}{y}\right)\right)\right) \]

       10. associate-*l* N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\left(x \cdot \left({t}^{2} \cdot \frac{1}{2}\right)\right), \left(\frac{\color{blue}{-1 \cdot \frac{x}{y} + t \cdot x}}{y}\right)\right)\right) \]

       11. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \left({t}^{2} \cdot \frac{1}{2}\right)\right), \left(\frac{\color{blue}{-1 \cdot \frac{x}{y} + t \cdot x}}{y}\right)\right)\right) \]

       12. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\left({t}^{2}\right), \frac{1}{2}\right)\right), \left(\frac{-1 \cdot \frac{x}{y} + \color{blue}{t \cdot x}}{y}\right)\right)\right) \]

       13. unpow2 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\left(t \cdot t\right), \frac{1}{2}\right)\right), \left(\frac{-1 \cdot \frac{x}{y} + \color{blue}{t} \cdot x}{y}\right)\right)\right) \]

       14. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, t\right), \frac{1}{2}\right)\right), \left(\frac{-1 \cdot \frac{x}{y} + \color{blue}{t} \cdot x}{y}\right)\right)\right) \]

       15. /-lowering-/.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, t\right), \frac{1}{2}\right)\right), \mathsf{/.f64}\left(\left(-1 \cdot \frac{x}{y} + t \cdot x\right), \color{blue}{y}\right)\right)\right) \]

   13. Simplified 65.7%

       \[\leadsto \color{blue}{\left(y \cdot y\right) \cdot \left(x \cdot \left(\left(t \cdot t\right) \cdot 0.5\right) - \frac{x \cdot t - \frac{x}{y}}{y}\right)} \]

   if 8.8000000000000004e-7 < y < 3.00000000000000002e146

   1. Initial program 96.7%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 96.7%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(t \cdot y\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\left(y \cdot t\right)\right)\right) \]

      2. *-lowering-*.f64 51.2%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, t\right)\right)\right) \]

   7. Simplified 51.2%

      \[\leadsto \frac{x}{e^{\color{blue}{y \cdot t}}} \]

   8. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x + y \cdot \left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) - t \cdot x\right)} \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot \left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) - t \cdot x\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) - t \cdot x\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right)\right), \color{blue}{\left(t \cdot x\right)}\right)\right)\right) \]

   10. Simplified 22.0%

       \[\leadsto \color{blue}{x + y \cdot \left(y \cdot \left(0.5 \cdot \left(x \cdot \left(t \cdot t\right)\right)\right) - x \cdot t\right)} \]

   11. Taylor expanded in y around -inf

       \[\leadsto \color{blue}{{y}^{2} \cdot \left(-1 \cdot \frac{-1 \cdot \frac{x}{y} + t \cdot x}{y} + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)} \]
   12. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left({y}^{2}\right), \color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{x}{y} + t \cdot x}{y} + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)}\right) \]

       2. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(y \cdot y\right), \left(\color{blue}{-1 \cdot \frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}} + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \left(\color{blue}{-1 \cdot \frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}} + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) \]

       4. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right) + \color{blue}{-1 \cdot \frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}}\right)\right) \]

       5. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right) + \left(\mathsf{neg}\left(\frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}\right)\right)\right)\right) \]

       6. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right) - \color{blue}{\frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}}\right)\right) \]

       7. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right), \color{blue}{\left(\frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}\right)}\right)\right) \]

       8. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\left(\left({t}^{2} \cdot x\right) \cdot \frac{1}{2}\right), \left(\frac{\color{blue}{-1 \cdot \frac{x}{y} + t \cdot x}}{y}\right)\right)\right) \]

       9. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\left(\left(x \cdot {t}^{2}\right) \cdot \frac{1}{2}\right), \left(\frac{\color{blue}{-1 \cdot \frac{x}{y}} + t \cdot x}{y}\right)\right)\right) \]

       10. associate-*l* N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\left(x \cdot \left({t}^{2} \cdot \frac{1}{2}\right)\right), \left(\frac{\color{blue}{-1 \cdot \frac{x}{y} + t \cdot x}}{y}\right)\right)\right) \]

       11. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \left({t}^{2} \cdot \frac{1}{2}\right)\right), \left(\frac{\color{blue}{-1 \cdot \frac{x}{y} + t \cdot x}}{y}\right)\right)\right) \]

       12. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\left({t}^{2}\right), \frac{1}{2}\right)\right), \left(\frac{-1 \cdot \frac{x}{y} + \color{blue}{t \cdot x}}{y}\right)\right)\right) \]

       13. unpow2 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\left(t \cdot t\right), \frac{1}{2}\right)\right), \left(\frac{-1 \cdot \frac{x}{y} + \color{blue}{t} \cdot x}{y}\right)\right)\right) \]

       14. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, t\right), \frac{1}{2}\right)\right), \left(\frac{-1 \cdot \frac{x}{y} + \color{blue}{t} \cdot x}{y}\right)\right)\right) \]

       15. /-lowering-/.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, t\right), \frac{1}{2}\right)\right), \mathsf{/.f64}\left(\left(-1 \cdot \frac{x}{y} + t \cdot x\right), \color{blue}{y}\right)\right)\right) \]

   13. Simplified 28.3%

       \[\leadsto \color{blue}{\left(y \cdot y\right) \cdot \left(x \cdot \left(\left(t \cdot t\right) \cdot 0.5\right) - \frac{x \cdot t - \frac{x}{y}}{y}\right)} \]

   14. Taylor expanded in t around inf

       \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \color{blue}{\left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)}\right) \]
   15. Step-by-step derivation

       1. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \left(\left(\frac{1}{2} \cdot {t}^{2}\right) \cdot \color{blue}{x}\right)\right) \]

       2. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \left(x \cdot \color{blue}{\left(\frac{1}{2} \cdot {t}^{2}\right)}\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{1}{2} \cdot {t}^{2}\right)}\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{\left({t}^{2}\right)}\right)\right)\right) \]

       5. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{2}, \left(t \cdot \color{blue}{t}\right)\right)\right)\right) \]

       6. *-lowering-*.f64 51.0%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(t, \color{blue}{t}\right)\right)\right)\right) \]

   16. Simplified 51.0%

       \[\leadsto \left(y \cdot y\right) \cdot \color{blue}{\left(x \cdot \left(0.5 \cdot \left(t \cdot t\right)\right)\right)} \]

   if 3.00000000000000002e146 < y < 7.19999999999999972e282

   1. Initial program 100.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(t \cdot y\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\left(y \cdot t\right)\right)\right) \]

      2. *-lowering-*.f64 56.4%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, t\right)\right)\right) \]

   7. Simplified 56.4%

      \[\leadsto \frac{x}{e^{\color{blue}{y \cdot t}}} \]

   8. Taylor expanded in t around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + t \cdot \left(y + \frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right)\right)}\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(t \cdot \left(y + \frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \color{blue}{\left(y + \frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right)}\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(y, \color{blue}{\left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right)}\right)\right)\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(y, \left(\left(\frac{1}{2} \cdot t\right) \cdot \color{blue}{{y}^{2}}\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(\left(\frac{1}{2} \cdot t\right), \color{blue}{\left({y}^{2}\right)}\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, t\right), \left({\color{blue}{y}}^{2}\right)\right)\right)\right)\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, t\right), \left(y \cdot \color{blue}{y}\right)\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 85.3%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, t\right), \mathsf{*.f64}\left(y, \color{blue}{y}\right)\right)\right)\right)\right)\right) \]

   10. Simplified 85.3%

       \[\leadsto \frac{x}{\color{blue}{1 + t \cdot \left(y + \left(0.5 \cdot t\right) \cdot \left(y \cdot y\right)\right)}} \]
3. Recombined 8 regimes into one program.

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+241}:\\ \;\;\;\;x + t \cdot \left(t \cdot \left(\left(x \cdot 0.5\right) \cdot \left(y \cdot y\right)\right) - x \cdot y\right)\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{+68}:\\ \;\;\;\;\frac{x}{t \cdot \left(y + t \cdot \left(\left(t \cdot 0.16666666666666666\right) \cdot \left(y \cdot \left(y \cdot y\right)\right) + 0.5 \cdot \left(y \cdot y\right)\right)\right) + 1}\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-55}:\\ \;\;\;\;\frac{2 \cdot \frac{x}{a \cdot a}}{b \cdot b}\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{-200}:\\ \;\;\;\;\frac{x}{b \cdot \left(a + b \cdot \left(0.16666666666666666 \cdot \left(b \cdot \left(a \cdot \left(a \cdot a\right)\right)\right) + 0.5 \cdot \left(a \cdot a\right)\right)\right) + 1}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-133}:\\ \;\;\;\;x + b \cdot \left(b \cdot \left(x \cdot \left(0.5 \cdot \left(a \cdot a\right)\right)\right) - x \cdot a\right)\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{-7}:\\ \;\;\;\;\left(y \cdot y\right) \cdot \left(x \cdot \left(\left(t \cdot t\right) \cdot 0.5\right) + \frac{\frac{x}{y} - x \cdot t}{y}\right)\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+146}:\\ \;\;\;\;\left(y \cdot y\right) \cdot \left(x \cdot \left(\left(t \cdot t\right) \cdot 0.5\right)\right)\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+282}:\\ \;\;\;\;\frac{x}{t \cdot \left(y + \left(y \cdot y\right) \cdot \left(t \cdot 0.5\right)\right) + 1}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \left(t \cdot \left(\left(x \cdot 0.5\right) \cdot \left(y \cdot y\right)\right) - x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 48.3% accurate, 5.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(\left(t \cdot t\right) \cdot 0.5\right)\\ t_2 := 0.5 \cdot \left(a \cdot a\right)\\ t_3 := \frac{x}{t \cdot \left(y + \left(y \cdot y\right) \cdot \left(t \cdot 0.5\right)\right) + 1}\\ t_4 := x + t \cdot \left(t \cdot \left(\left(x \cdot 0.5\right) \cdot \left(y \cdot y\right)\right) - x \cdot y\right)\\ \mathbf{if}\;y \leq -9 \cdot 10^{+241}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{+72}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-55}:\\ \;\;\;\;\frac{2 \cdot \frac{x}{a \cdot a}}{b \cdot b}\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-200}:\\ \;\;\;\;\frac{x}{b \cdot \left(a + b \cdot \left(0.16666666666666666 \cdot \left(b \cdot \left(a \cdot \left(a \cdot a\right)\right)\right) + t\_2\right)\right) + 1}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-133}:\\ \;\;\;\;x + b \cdot \left(b \cdot \left(x \cdot t\_2\right) - x \cdot a\right)\\ \mathbf{elif}\;y \leq 0.00032:\\ \;\;\;\;\left(y \cdot y\right) \cdot \left(t\_1 + \frac{\frac{x}{y} - x \cdot t}{y}\right)\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{+145}:\\ \;\;\;\;\left(y \cdot y\right) \cdot t\_1\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+282}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (* (* t t) 0.5)))
        (t_2 (* 0.5 (* a a)))
        (t_3 (/ x (+ (* t (+ y (* (* y y) (* t 0.5)))) 1.0)))
        (t_4 (+ x (* t (- (* t (* (* x 0.5) (* y y))) (* x y))))))
   (if (<= y -9e+241)
     t_4
     (if (<= y -1.6e+72)
       t_3
       (if (<= y -2.3e-55)
         (/ (* 2.0 (/ x (* a a))) (* b b))
         (if (<= y -1.2e-200)
           (/
            x
            (+
             (*
              b
              (+ a (* b (+ (* 0.16666666666666666 (* b (* a (* a a)))) t_2))))
             1.0))
           (if (<= y 1.8e-133)
             (+ x (* b (- (* b (* x t_2)) (* x a))))
             (if (<= y 0.00032)
               (* (* y y) (+ t_1 (/ (- (/ x y) (* x t)) y)))
               (if (<= y 5.4e+145)
                 (* (* y y) t_1)
                 (if (<= y 4.6e+282) t_3 t_4))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * ((t * t) * 0.5);
	double t_2 = 0.5 * (a * a);
	double t_3 = x / ((t * (y + ((y * y) * (t * 0.5)))) + 1.0);
	double t_4 = x + (t * ((t * ((x * 0.5) * (y * y))) - (x * y)));
	double tmp;
	if (y <= -9e+241) {
		tmp = t_4;
	} else if (y <= -1.6e+72) {
		tmp = t_3;
	} else if (y <= -2.3e-55) {
		tmp = (2.0 * (x / (a * a))) / (b * b);
	} else if (y <= -1.2e-200) {
		tmp = x / ((b * (a + (b * ((0.16666666666666666 * (b * (a * (a * a)))) + t_2)))) + 1.0);
	} else if (y <= 1.8e-133) {
		tmp = x + (b * ((b * (x * t_2)) - (x * a)));
	} else if (y <= 0.00032) {
		tmp = (y * y) * (t_1 + (((x / y) - (x * t)) / y));
	} else if (y <= 5.4e+145) {
		tmp = (y * y) * t_1;
	} else if (y <= 4.6e+282) {
		tmp = t_3;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = x * ((t * t) * 0.5d0)
    t_2 = 0.5d0 * (a * a)
    t_3 = x / ((t * (y + ((y * y) * (t * 0.5d0)))) + 1.0d0)
    t_4 = x + (t * ((t * ((x * 0.5d0) * (y * y))) - (x * y)))
    if (y <= (-9d+241)) then
        tmp = t_4
    else if (y <= (-1.6d+72)) then
        tmp = t_3
    else if (y <= (-2.3d-55)) then
        tmp = (2.0d0 * (x / (a * a))) / (b * b)
    else if (y <= (-1.2d-200)) then
        tmp = x / ((b * (a + (b * ((0.16666666666666666d0 * (b * (a * (a * a)))) + t_2)))) + 1.0d0)
    else if (y <= 1.8d-133) then
        tmp = x + (b * ((b * (x * t_2)) - (x * a)))
    else if (y <= 0.00032d0) then
        tmp = (y * y) * (t_1 + (((x / y) - (x * t)) / y))
    else if (y <= 5.4d+145) then
        tmp = (y * y) * t_1
    else if (y <= 4.6d+282) then
        tmp = t_3
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * ((t * t) * 0.5);
	double t_2 = 0.5 * (a * a);
	double t_3 = x / ((t * (y + ((y * y) * (t * 0.5)))) + 1.0);
	double t_4 = x + (t * ((t * ((x * 0.5) * (y * y))) - (x * y)));
	double tmp;
	if (y <= -9e+241) {
		tmp = t_4;
	} else if (y <= -1.6e+72) {
		tmp = t_3;
	} else if (y <= -2.3e-55) {
		tmp = (2.0 * (x / (a * a))) / (b * b);
	} else if (y <= -1.2e-200) {
		tmp = x / ((b * (a + (b * ((0.16666666666666666 * (b * (a * (a * a)))) + t_2)))) + 1.0);
	} else if (y <= 1.8e-133) {
		tmp = x + (b * ((b * (x * t_2)) - (x * a)));
	} else if (y <= 0.00032) {
		tmp = (y * y) * (t_1 + (((x / y) - (x * t)) / y));
	} else if (y <= 5.4e+145) {
		tmp = (y * y) * t_1;
	} else if (y <= 4.6e+282) {
		tmp = t_3;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * ((t * t) * 0.5)
	t_2 = 0.5 * (a * a)
	t_3 = x / ((t * (y + ((y * y) * (t * 0.5)))) + 1.0)
	t_4 = x + (t * ((t * ((x * 0.5) * (y * y))) - (x * y)))
	tmp = 0
	if y <= -9e+241:
		tmp = t_4
	elif y <= -1.6e+72:
		tmp = t_3
	elif y <= -2.3e-55:
		tmp = (2.0 * (x / (a * a))) / (b * b)
	elif y <= -1.2e-200:
		tmp = x / ((b * (a + (b * ((0.16666666666666666 * (b * (a * (a * a)))) + t_2)))) + 1.0)
	elif y <= 1.8e-133:
		tmp = x + (b * ((b * (x * t_2)) - (x * a)))
	elif y <= 0.00032:
		tmp = (y * y) * (t_1 + (((x / y) - (x * t)) / y))
	elif y <= 5.4e+145:
		tmp = (y * y) * t_1
	elif y <= 4.6e+282:
		tmp = t_3
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * Float64(Float64(t * t) * 0.5))
	t_2 = Float64(0.5 * Float64(a * a))
	t_3 = Float64(x / Float64(Float64(t * Float64(y + Float64(Float64(y * y) * Float64(t * 0.5)))) + 1.0))
	t_4 = Float64(x + Float64(t * Float64(Float64(t * Float64(Float64(x * 0.5) * Float64(y * y))) - Float64(x * y))))
	tmp = 0.0
	if (y <= -9e+241)
		tmp = t_4;
	elseif (y <= -1.6e+72)
		tmp = t_3;
	elseif (y <= -2.3e-55)
		tmp = Float64(Float64(2.0 * Float64(x / Float64(a * a))) / Float64(b * b));
	elseif (y <= -1.2e-200)
		tmp = Float64(x / Float64(Float64(b * Float64(a + Float64(b * Float64(Float64(0.16666666666666666 * Float64(b * Float64(a * Float64(a * a)))) + t_2)))) + 1.0));
	elseif (y <= 1.8e-133)
		tmp = Float64(x + Float64(b * Float64(Float64(b * Float64(x * t_2)) - Float64(x * a))));
	elseif (y <= 0.00032)
		tmp = Float64(Float64(y * y) * Float64(t_1 + Float64(Float64(Float64(x / y) - Float64(x * t)) / y)));
	elseif (y <= 5.4e+145)
		tmp = Float64(Float64(y * y) * t_1);
	elseif (y <= 4.6e+282)
		tmp = t_3;
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * ((t * t) * 0.5);
	t_2 = 0.5 * (a * a);
	t_3 = x / ((t * (y + ((y * y) * (t * 0.5)))) + 1.0);
	t_4 = x + (t * ((t * ((x * 0.5) * (y * y))) - (x * y)));
	tmp = 0.0;
	if (y <= -9e+241)
		tmp = t_4;
	elseif (y <= -1.6e+72)
		tmp = t_3;
	elseif (y <= -2.3e-55)
		tmp = (2.0 * (x / (a * a))) / (b * b);
	elseif (y <= -1.2e-200)
		tmp = x / ((b * (a + (b * ((0.16666666666666666 * (b * (a * (a * a)))) + t_2)))) + 1.0);
	elseif (y <= 1.8e-133)
		tmp = x + (b * ((b * (x * t_2)) - (x * a)));
	elseif (y <= 0.00032)
		tmp = (y * y) * (t_1 + (((x / y) - (x * t)) / y));
	elseif (y <= 5.4e+145)
		tmp = (y * y) * t_1;
	elseif (y <= 4.6e+282)
		tmp = t_3;
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[(N[(t * t), $MachinePrecision] * 0.5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(0.5 * N[(a * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x / N[(N[(t * N[(y + N[(N[(y * y), $MachinePrecision] * N[(t * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(x + N[(t * N[(N[(t * N[(N[(x * 0.5), $MachinePrecision] * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9e+241], t$95$4, If[LessEqual[y, -1.6e+72], t$95$3, If[LessEqual[y, -2.3e-55], N[(N[(2.0 * N[(x / N[(a * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(b * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.2e-200], N[(x / N[(N[(b * N[(a + N[(b * N[(N[(0.16666666666666666 * N[(b * N[(a * N[(a * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.8e-133], N[(x + N[(b * N[(N[(b * N[(x * t$95$2), $MachinePrecision]), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 0.00032], N[(N[(y * y), $MachinePrecision] * N[(t$95$1 + N[(N[(N[(x / y), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.4e+145], N[(N[(y * y), $MachinePrecision] * t$95$1), $MachinePrecision], If[LessEqual[y, 4.6e+282], t$95$3, t$95$4]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y < -8.99999999999999987e241 or 4.60000000000000002e282 < y

   1. Initial program 100.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(t \cdot y\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\left(y \cdot t\right)\right)\right) \]

      2. *-lowering-*.f64 61.7%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, t\right)\right)\right) \]

   7. Simplified 61.7%

      \[\leadsto \frac{x}{e^{\color{blue}{y \cdot t}}} \]

   8. Taylor expanded in t around 0

      \[\leadsto \color{blue}{x + t \cdot \left(-1 \cdot \left(t \cdot \left(-1 \cdot \left(x \cdot {y}^{2}\right) + \frac{1}{2} \cdot \left(x \cdot {y}^{2}\right)\right)\right) - x \cdot y\right)} \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(t \cdot \left(-1 \cdot \left(t \cdot \left(-1 \cdot \left(x \cdot {y}^{2}\right) + \frac{1}{2} \cdot \left(x \cdot {y}^{2}\right)\right)\right) - x \cdot y\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(t, \color{blue}{\left(-1 \cdot \left(t \cdot \left(-1 \cdot \left(x \cdot {y}^{2}\right) + \frac{1}{2} \cdot \left(x \cdot {y}^{2}\right)\right)\right) - x \cdot y\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(-1 \cdot \left(t \cdot \left(-1 \cdot \left(x \cdot {y}^{2}\right) + \frac{1}{2} \cdot \left(x \cdot {y}^{2}\right)\right)\right)\right), \color{blue}{\left(x \cdot y\right)}\right)\right)\right) \]

   10. Simplified 69.8%

       \[\leadsto \color{blue}{x + t \cdot \left(t \cdot \left(\left(0.5 \cdot x\right) \cdot \left(y \cdot y\right)\right) - x \cdot y\right)} \]

   if -8.99999999999999987e241 < y < -1.6000000000000001e72 or 5.40000000000000044e145 < y < 4.60000000000000002e282

   1. Initial program 100.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(t \cdot y\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\left(y \cdot t\right)\right)\right) \]

      2. *-lowering-*.f64 71.7%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, t\right)\right)\right) \]

   7. Simplified 71.7%

      \[\leadsto \frac{x}{e^{\color{blue}{y \cdot t}}} \]

   8. Taylor expanded in t around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + t \cdot \left(y + \frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right)\right)}\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(t \cdot \left(y + \frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \color{blue}{\left(y + \frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right)}\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(y, \color{blue}{\left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right)}\right)\right)\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(y, \left(\left(\frac{1}{2} \cdot t\right) \cdot \color{blue}{{y}^{2}}\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(\left(\frac{1}{2} \cdot t\right), \color{blue}{\left({y}^{2}\right)}\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, t\right), \left({\color{blue}{y}}^{2}\right)\right)\right)\right)\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, t\right), \left(y \cdot \color{blue}{y}\right)\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 71.6%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, t\right), \mathsf{*.f64}\left(y, \color{blue}{y}\right)\right)\right)\right)\right)\right) \]

   10. Simplified 71.6%

       \[\leadsto \frac{x}{\color{blue}{1 + t \cdot \left(y + \left(0.5 \cdot t\right) \cdot \left(y \cdot y\right)\right)}} \]

   if -1.6000000000000001e72 < y < -2.30000000000000011e-55

   1. Initial program 96.6%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 96.6%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(a \cdot b\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 42.4%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, b\right)\right)\right) \]

   7. Simplified 42.4%

      \[\leadsto \frac{x}{e^{\color{blue}{a \cdot b}}} \]

   8. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + b \cdot \left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)\right)}\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(b \cdot \left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \color{blue}{\left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \color{blue}{\left(\frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right)\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(\left(\frac{1}{2} \cdot {a}^{2}\right) \cdot \color{blue}{b}\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\left(\frac{1}{2} \cdot {a}^{2}\right), \color{blue}{b}\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left({a}^{2}\right)\right), b\right)\right)\right)\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left(a \cdot a\right)\right), b\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 22.2%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(a, a\right)\right), b\right)\right)\right)\right)\right) \]

   10. Simplified 22.2%

       \[\leadsto \frac{x}{\color{blue}{1 + b \cdot \left(a + \left(0.5 \cdot \left(a \cdot a\right)\right) \cdot b\right)}} \]
   11. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(b \cdot \color{blue}{\left(\frac{1}{2} \cdot \left(a \cdot a\right)\right)}\right)\right)\right)\right)\right) \]

       2. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(b \cdot \left(\left(\frac{1}{2} \cdot a\right) \cdot \color{blue}{a}\right)\right)\right)\right)\right)\right) \]

       3. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(\left(b \cdot \left(\frac{1}{2} \cdot a\right)\right) \cdot \color{blue}{a}\right)\right)\right)\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\left(b \cdot \left(\frac{1}{2} \cdot a\right)\right), \color{blue}{a}\right)\right)\right)\right)\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \left(\frac{1}{2} \cdot a\right)\right), a\right)\right)\right)\right)\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \left(a \cdot \frac{1}{2}\right)\right), a\right)\right)\right)\right)\right) \]

       7. *-lowering-*.f64 22.2%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \frac{1}{2}\right)\right), a\right)\right)\right)\right)\right) \]

   12. Applied egg-rr 22.2%

       \[\leadsto \frac{x}{1 + b \cdot \left(a + \color{blue}{\left(b \cdot \left(a \cdot 0.5\right)\right) \cdot a}\right)} \]

   13. Taylor expanded in b around inf

       \[\leadsto \color{blue}{2 \cdot \frac{x}{{a}^{2} \cdot {b}^{2}}} \]
   14. Step-by-step derivation

       1. associate-/r* N/A

          \[\leadsto 2 \cdot \frac{\frac{x}{{a}^{2}}}{\color{blue}{{b}^{2}}} \]

       2. associate-*r/ N/A

          \[\leadsto \frac{2 \cdot \frac{x}{{a}^{2}}}{\color{blue}{{b}^{2}}} \]

       3. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left(2 \cdot \frac{x}{{a}^{2}}\right), \color{blue}{\left({b}^{2}\right)}\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(2, \left(\frac{x}{{a}^{2}}\right)\right), \left({\color{blue}{b}}^{2}\right)\right) \]

       5. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(2, \mathsf{/.f64}\left(x, \left({a}^{2}\right)\right)\right), \left({b}^{2}\right)\right) \]

       6. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(2, \mathsf{/.f64}\left(x, \left(a \cdot a\right)\right)\right), \left({b}^{2}\right)\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(2, \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, a\right)\right)\right), \left({b}^{2}\right)\right) \]

       8. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(2, \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, a\right)\right)\right), \left(b \cdot \color{blue}{b}\right)\right) \]

       9. *-lowering-*.f64 52.7%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(2, \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, a\right)\right)\right), \mathsf{*.f64}\left(b, \color{blue}{b}\right)\right) \]

   15. Simplified 52.7%

       \[\leadsto \color{blue}{\frac{2 \cdot \frac{x}{a \cdot a}}{b \cdot b}} \]

   if -2.30000000000000011e-55 < y < -1.20000000000000001e-200

   1. Initial program 91.4%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 91.4%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(a \cdot b\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 71.8%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, b\right)\right)\right) \]

   7. Simplified 71.8%

      \[\leadsto \frac{x}{e^{\color{blue}{a \cdot b}}} \]

   8. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + b \cdot \left(a + b \cdot \left(\frac{1}{6} \cdot \left({a}^{3} \cdot b\right) + \frac{1}{2} \cdot {a}^{2}\right)\right)\right)}\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(b \cdot \left(a + b \cdot \left(\frac{1}{6} \cdot \left({a}^{3} \cdot b\right) + \frac{1}{2} \cdot {a}^{2}\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \color{blue}{\left(a + b \cdot \left(\frac{1}{6} \cdot \left({a}^{3} \cdot b\right) + \frac{1}{2} \cdot {a}^{2}\right)\right)}\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \color{blue}{\left(b \cdot \left(\frac{1}{6} \cdot \left({a}^{3} \cdot b\right) + \frac{1}{2} \cdot {a}^{2}\right)\right)}\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \color{blue}{\left(\frac{1}{6} \cdot \left({a}^{3} \cdot b\right) + \frac{1}{2} \cdot {a}^{2}\right)}\right)\right)\right)\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\left(\frac{1}{6} \cdot \left({a}^{3} \cdot b\right)\right), \color{blue}{\left(\frac{1}{2} \cdot {a}^{2}\right)}\right)\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, \left({a}^{3} \cdot b\right)\right), \left(\color{blue}{\frac{1}{2}} \cdot {a}^{2}\right)\right)\right)\right)\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, \left(b \cdot {a}^{3}\right)\right), \left(\frac{1}{2} \cdot {a}^{2}\right)\right)\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, \mathsf{*.f64}\left(b, \left({a}^{3}\right)\right)\right), \left(\frac{1}{2} \cdot {a}^{2}\right)\right)\right)\right)\right)\right)\right) \]

      9. cube-mult N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, \mathsf{*.f64}\left(b, \left(a \cdot \left(a \cdot a\right)\right)\right)\right), \left(\frac{1}{2} \cdot {a}^{2}\right)\right)\right)\right)\right)\right)\right) \]

      10. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, \mathsf{*.f64}\left(b, \left(a \cdot {a}^{2}\right)\right)\right), \left(\frac{1}{2} \cdot {a}^{2}\right)\right)\right)\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \left({a}^{2}\right)\right)\right)\right), \left(\frac{1}{2} \cdot {a}^{2}\right)\right)\right)\right)\right)\right)\right) \]

      12. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \left(a \cdot a\right)\right)\right)\right), \left(\frac{1}{2} \cdot {a}^{2}\right)\right)\right)\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(a, a\right)\right)\right)\right), \left(\frac{1}{2} \cdot {a}^{2}\right)\right)\right)\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(a, a\right)\right)\right)\right), \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{\left({a}^{2}\right)}\right)\right)\right)\right)\right)\right)\right) \]

      15. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(a, a\right)\right)\right)\right), \mathsf{*.f64}\left(\frac{1}{2}, \left(a \cdot \color{blue}{a}\right)\right)\right)\right)\right)\right)\right)\right) \]

      16. *-lowering-*.f64 62.7%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(a, a\right)\right)\right)\right), \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(a, \color{blue}{a}\right)\right)\right)\right)\right)\right)\right)\right) \]

   10. Simplified 62.7%

       \[\leadsto \frac{x}{\color{blue}{1 + b \cdot \left(a + b \cdot \left(0.16666666666666666 \cdot \left(b \cdot \left(a \cdot \left(a \cdot a\right)\right)\right) + 0.5 \cdot \left(a \cdot a\right)\right)\right)}} \]

   if -1.20000000000000001e-200 < y < 1.8000000000000002e-133

   1. Initial program 94.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 94.0%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(a \cdot b\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 89.6%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, b\right)\right)\right) \]

   7. Simplified 89.6%

      \[\leadsto \frac{x}{e^{\color{blue}{a \cdot b}}} \]

   8. Taylor expanded in b around 0

      \[\leadsto \color{blue}{x + b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left({a}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({a}^{2} \cdot x\right)\right)\right) - a \cdot x\right)} \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left({a}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({a}^{2} \cdot x\right)\right)\right) - a \cdot x\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \color{blue}{\left(-1 \cdot \left(b \cdot \left(-1 \cdot \left({a}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({a}^{2} \cdot x\right)\right)\right) - a \cdot x\right)}\right)\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(\left(\mathsf{neg}\left(b \cdot \left(-1 \cdot \left({a}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({a}^{2} \cdot x\right)\right)\right)\right) - \color{blue}{a} \cdot x\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(b \cdot \left(\mathsf{neg}\left(\left(-1 \cdot \left({a}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({a}^{2} \cdot x\right)\right)\right)\right) - \color{blue}{a} \cdot x\right)\right)\right) \]

      5. distribute-rgt-out N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(b \cdot \left(\mathsf{neg}\left(\left({a}^{2} \cdot x\right) \cdot \left(-1 + \frac{1}{2}\right)\right)\right) - a \cdot x\right)\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(b \cdot \left(\mathsf{neg}\left(\left({a}^{2} \cdot x\right) \cdot \frac{-1}{2}\right)\right) - a \cdot x\right)\right)\right) \]

      7. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(b \cdot \left(\left({a}^{2} \cdot x\right) \cdot \left(\mathsf{neg}\left(\frac{-1}{2}\right)\right)\right) - a \cdot x\right)\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(b \cdot \left(\left({a}^{2} \cdot x\right) \cdot \frac{1}{2}\right) - a \cdot x\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(b \cdot \left(\frac{1}{2} \cdot \left({a}^{2} \cdot x\right)\right) - a \cdot x\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(b \cdot \left(\frac{1}{2} \cdot \left({a}^{2} \cdot x\right)\right)\right), \color{blue}{\left(a \cdot x\right)}\right)\right)\right) \]

   10. Simplified 67.1%

       \[\leadsto \color{blue}{x + b \cdot \left(b \cdot \left(\left(0.5 \cdot \left(a \cdot a\right)\right) \cdot x\right) - x \cdot a\right)} \]

   if 1.8000000000000002e-133 < y < 3.20000000000000026e-4

   1. Initial program 96.3%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 96.4%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(t \cdot y\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\left(y \cdot t\right)\right)\right) \]

      2. *-lowering-*.f64 66.3%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, t\right)\right)\right) \]

   7. Simplified 66.3%

      \[\leadsto \frac{x}{e^{\color{blue}{y \cdot t}}} \]

   8. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x + y \cdot \left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) - t \cdot x\right)} \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot \left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) - t \cdot x\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) - t \cdot x\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right)\right), \color{blue}{\left(t \cdot x\right)}\right)\right)\right) \]

   10. Simplified 58.9%

       \[\leadsto \color{blue}{x + y \cdot \left(y \cdot \left(0.5 \cdot \left(x \cdot \left(t \cdot t\right)\right)\right) - x \cdot t\right)} \]

   11. Taylor expanded in y around -inf

       \[\leadsto \color{blue}{{y}^{2} \cdot \left(-1 \cdot \frac{-1 \cdot \frac{x}{y} + t \cdot x}{y} + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)} \]
   12. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left({y}^{2}\right), \color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{x}{y} + t \cdot x}{y} + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)}\right) \]

       2. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(y \cdot y\right), \left(\color{blue}{-1 \cdot \frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}} + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \left(\color{blue}{-1 \cdot \frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}} + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) \]

       4. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right) + \color{blue}{-1 \cdot \frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}}\right)\right) \]

       5. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right) + \left(\mathsf{neg}\left(\frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}\right)\right)\right)\right) \]

       6. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right) - \color{blue}{\frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}}\right)\right) \]

       7. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right), \color{blue}{\left(\frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}\right)}\right)\right) \]

       8. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\left(\left({t}^{2} \cdot x\right) \cdot \frac{1}{2}\right), \left(\frac{\color{blue}{-1 \cdot \frac{x}{y} + t \cdot x}}{y}\right)\right)\right) \]

       9. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\left(\left(x \cdot {t}^{2}\right) \cdot \frac{1}{2}\right), \left(\frac{\color{blue}{-1 \cdot \frac{x}{y}} + t \cdot x}{y}\right)\right)\right) \]

       10. associate-*l* N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\left(x \cdot \left({t}^{2} \cdot \frac{1}{2}\right)\right), \left(\frac{\color{blue}{-1 \cdot \frac{x}{y} + t \cdot x}}{y}\right)\right)\right) \]

       11. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \left({t}^{2} \cdot \frac{1}{2}\right)\right), \left(\frac{\color{blue}{-1 \cdot \frac{x}{y} + t \cdot x}}{y}\right)\right)\right) \]

       12. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\left({t}^{2}\right), \frac{1}{2}\right)\right), \left(\frac{-1 \cdot \frac{x}{y} + \color{blue}{t \cdot x}}{y}\right)\right)\right) \]

       13. unpow2 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\left(t \cdot t\right), \frac{1}{2}\right)\right), \left(\frac{-1 \cdot \frac{x}{y} + \color{blue}{t} \cdot x}{y}\right)\right)\right) \]

       14. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, t\right), \frac{1}{2}\right)\right), \left(\frac{-1 \cdot \frac{x}{y} + \color{blue}{t} \cdot x}{y}\right)\right)\right) \]

       15. /-lowering-/.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, t\right), \frac{1}{2}\right)\right), \mathsf{/.f64}\left(\left(-1 \cdot \frac{x}{y} + t \cdot x\right), \color{blue}{y}\right)\right)\right) \]

   13. Simplified 65.7%

       \[\leadsto \color{blue}{\left(y \cdot y\right) \cdot \left(x \cdot \left(\left(t \cdot t\right) \cdot 0.5\right) - \frac{x \cdot t - \frac{x}{y}}{y}\right)} \]

   if 3.20000000000000026e-4 < y < 5.40000000000000044e145

   1. Initial program 96.7%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 96.7%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(t \cdot y\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\left(y \cdot t\right)\right)\right) \]

      2. *-lowering-*.f64 51.2%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, t\right)\right)\right) \]

   7. Simplified 51.2%

      \[\leadsto \frac{x}{e^{\color{blue}{y \cdot t}}} \]

   8. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x + y \cdot \left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) - t \cdot x\right)} \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot \left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) - t \cdot x\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) - t \cdot x\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right)\right), \color{blue}{\left(t \cdot x\right)}\right)\right)\right) \]

   10. Simplified 22.0%

       \[\leadsto \color{blue}{x + y \cdot \left(y \cdot \left(0.5 \cdot \left(x \cdot \left(t \cdot t\right)\right)\right) - x \cdot t\right)} \]

   11. Taylor expanded in y around -inf

       \[\leadsto \color{blue}{{y}^{2} \cdot \left(-1 \cdot \frac{-1 \cdot \frac{x}{y} + t \cdot x}{y} + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)} \]
   12. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left({y}^{2}\right), \color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{x}{y} + t \cdot x}{y} + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)}\right) \]

       2. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(y \cdot y\right), \left(\color{blue}{-1 \cdot \frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}} + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \left(\color{blue}{-1 \cdot \frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}} + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) \]

       4. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right) + \color{blue}{-1 \cdot \frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}}\right)\right) \]

       5. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right) + \left(\mathsf{neg}\left(\frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}\right)\right)\right)\right) \]

       6. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right) - \color{blue}{\frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}}\right)\right) \]

       7. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right), \color{blue}{\left(\frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}\right)}\right)\right) \]

       8. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\left(\left({t}^{2} \cdot x\right) \cdot \frac{1}{2}\right), \left(\frac{\color{blue}{-1 \cdot \frac{x}{y} + t \cdot x}}{y}\right)\right)\right) \]

       9. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\left(\left(x \cdot {t}^{2}\right) \cdot \frac{1}{2}\right), \left(\frac{\color{blue}{-1 \cdot \frac{x}{y}} + t \cdot x}{y}\right)\right)\right) \]

       10. associate-*l* N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\left(x \cdot \left({t}^{2} \cdot \frac{1}{2}\right)\right), \left(\frac{\color{blue}{-1 \cdot \frac{x}{y} + t \cdot x}}{y}\right)\right)\right) \]

       11. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \left({t}^{2} \cdot \frac{1}{2}\right)\right), \left(\frac{\color{blue}{-1 \cdot \frac{x}{y} + t \cdot x}}{y}\right)\right)\right) \]

       12. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\left({t}^{2}\right), \frac{1}{2}\right)\right), \left(\frac{-1 \cdot \frac{x}{y} + \color{blue}{t \cdot x}}{y}\right)\right)\right) \]

       13. unpow2 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\left(t \cdot t\right), \frac{1}{2}\right)\right), \left(\frac{-1 \cdot \frac{x}{y} + \color{blue}{t} \cdot x}{y}\right)\right)\right) \]

       14. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, t\right), \frac{1}{2}\right)\right), \left(\frac{-1 \cdot \frac{x}{y} + \color{blue}{t} \cdot x}{y}\right)\right)\right) \]

       15. /-lowering-/.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, t\right), \frac{1}{2}\right)\right), \mathsf{/.f64}\left(\left(-1 \cdot \frac{x}{y} + t \cdot x\right), \color{blue}{y}\right)\right)\right) \]

   13. Simplified 28.3%

       \[\leadsto \color{blue}{\left(y \cdot y\right) \cdot \left(x \cdot \left(\left(t \cdot t\right) \cdot 0.5\right) - \frac{x \cdot t - \frac{x}{y}}{y}\right)} \]

   14. Taylor expanded in t around inf

       \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \color{blue}{\left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)}\right) \]
   15. Step-by-step derivation

       1. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \left(\left(\frac{1}{2} \cdot {t}^{2}\right) \cdot \color{blue}{x}\right)\right) \]

       2. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \left(x \cdot \color{blue}{\left(\frac{1}{2} \cdot {t}^{2}\right)}\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{1}{2} \cdot {t}^{2}\right)}\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{\left({t}^{2}\right)}\right)\right)\right) \]

       5. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{2}, \left(t \cdot \color{blue}{t}\right)\right)\right)\right) \]

       6. *-lowering-*.f64 51.0%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(t, \color{blue}{t}\right)\right)\right)\right) \]

   16. Simplified 51.0%

       \[\leadsto \left(y \cdot y\right) \cdot \color{blue}{\left(x \cdot \left(0.5 \cdot \left(t \cdot t\right)\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+241}:\\ \;\;\;\;x + t \cdot \left(t \cdot \left(\left(x \cdot 0.5\right) \cdot \left(y \cdot y\right)\right) - x \cdot y\right)\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{+72}:\\ \;\;\;\;\frac{x}{t \cdot \left(y + \left(y \cdot y\right) \cdot \left(t \cdot 0.5\right)\right) + 1}\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-55}:\\ \;\;\;\;\frac{2 \cdot \frac{x}{a \cdot a}}{b \cdot b}\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-200}:\\ \;\;\;\;\frac{x}{b \cdot \left(a + b \cdot \left(0.16666666666666666 \cdot \left(b \cdot \left(a \cdot \left(a \cdot a\right)\right)\right) + 0.5 \cdot \left(a \cdot a\right)\right)\right) + 1}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-133}:\\ \;\;\;\;x + b \cdot \left(b \cdot \left(x \cdot \left(0.5 \cdot \left(a \cdot a\right)\right)\right) - x \cdot a\right)\\ \mathbf{elif}\;y \leq 0.00032:\\ \;\;\;\;\left(y \cdot y\right) \cdot \left(x \cdot \left(\left(t \cdot t\right) \cdot 0.5\right) + \frac{\frac{x}{y} - x \cdot t}{y}\right)\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{+145}:\\ \;\;\;\;\left(y \cdot y\right) \cdot \left(x \cdot \left(\left(t \cdot t\right) \cdot 0.5\right)\right)\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+282}:\\ \;\;\;\;\frac{x}{t \cdot \left(y + \left(y \cdot y\right) \cdot \left(t \cdot 0.5\right)\right) + 1}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \left(t \cdot \left(\left(x \cdot 0.5\right) \cdot \left(y \cdot y\right)\right) - x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 48.2% accurate, 5.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(\left(t \cdot t\right) \cdot 0.5\right)\\ t_2 := \frac{x}{t \cdot \left(y + \left(y \cdot y\right) \cdot \left(t \cdot 0.5\right)\right) + 1}\\ t_3 := x + t \cdot \left(t \cdot \left(\left(x \cdot 0.5\right) \cdot \left(y \cdot y\right)\right) - x \cdot y\right)\\ \mathbf{if}\;y \leq -8 \cdot 10^{+241}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{+75}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-55}:\\ \;\;\;\;\frac{2 \cdot \frac{x}{a \cdot a}}{b \cdot b}\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-201}:\\ \;\;\;\;\frac{x}{a \cdot \left(b + a \cdot \left(\left(a \cdot 0.16666666666666666\right) \cdot \left(b \cdot \left(b \cdot b\right)\right) + 0.5 \cdot \left(b \cdot b\right)\right)\right) + 1}\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-133}:\\ \;\;\;\;x + b \cdot \left(b \cdot \left(x \cdot \left(0.5 \cdot \left(a \cdot a\right)\right)\right) - x \cdot a\right)\\ \mathbf{elif}\;y \leq 0.00019:\\ \;\;\;\;\left(y \cdot y\right) \cdot \left(t\_1 + \frac{\frac{x}{y} - x \cdot t}{y}\right)\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+144}:\\ \;\;\;\;\left(y \cdot y\right) \cdot t\_1\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+282}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (* (* t t) 0.5)))
        (t_2 (/ x (+ (* t (+ y (* (* y y) (* t 0.5)))) 1.0)))
        (t_3 (+ x (* t (- (* t (* (* x 0.5) (* y y))) (* x y))))))
   (if (<= y -8e+241)
     t_3
     (if (<= y -1.25e+75)
       t_2
       (if (<= y -2.3e-55)
         (/ (* 2.0 (/ x (* a a))) (* b b))
         (if (<= y -2.5e-201)
           (/
            x
            (+
             (*
              a
              (+
               b
               (*
                a
                (+
                 (* (* a 0.16666666666666666) (* b (* b b)))
                 (* 0.5 (* b b))))))
             1.0))
           (if (<= y 1.55e-133)
             (+ x (* b (- (* b (* x (* 0.5 (* a a)))) (* x a))))
             (if (<= y 0.00019)
               (* (* y y) (+ t_1 (/ (- (/ x y) (* x t)) y)))
               (if (<= y 2.8e+144)
                 (* (* y y) t_1)
                 (if (<= y 7.2e+282) t_2 t_3))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * ((t * t) * 0.5);
	double t_2 = x / ((t * (y + ((y * y) * (t * 0.5)))) + 1.0);
	double t_3 = x + (t * ((t * ((x * 0.5) * (y * y))) - (x * y)));
	double tmp;
	if (y <= -8e+241) {
		tmp = t_3;
	} else if (y <= -1.25e+75) {
		tmp = t_2;
	} else if (y <= -2.3e-55) {
		tmp = (2.0 * (x / (a * a))) / (b * b);
	} else if (y <= -2.5e-201) {
		tmp = x / ((a * (b + (a * (((a * 0.16666666666666666) * (b * (b * b))) + (0.5 * (b * b)))))) + 1.0);
	} else if (y <= 1.55e-133) {
		tmp = x + (b * ((b * (x * (0.5 * (a * a)))) - (x * a)));
	} else if (y <= 0.00019) {
		tmp = (y * y) * (t_1 + (((x / y) - (x * t)) / y));
	} else if (y <= 2.8e+144) {
		tmp = (y * y) * t_1;
	} else if (y <= 7.2e+282) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x * ((t * t) * 0.5d0)
    t_2 = x / ((t * (y + ((y * y) * (t * 0.5d0)))) + 1.0d0)
    t_3 = x + (t * ((t * ((x * 0.5d0) * (y * y))) - (x * y)))
    if (y <= (-8d+241)) then
        tmp = t_3
    else if (y <= (-1.25d+75)) then
        tmp = t_2
    else if (y <= (-2.3d-55)) then
        tmp = (2.0d0 * (x / (a * a))) / (b * b)
    else if (y <= (-2.5d-201)) then
        tmp = x / ((a * (b + (a * (((a * 0.16666666666666666d0) * (b * (b * b))) + (0.5d0 * (b * b)))))) + 1.0d0)
    else if (y <= 1.55d-133) then
        tmp = x + (b * ((b * (x * (0.5d0 * (a * a)))) - (x * a)))
    else if (y <= 0.00019d0) then
        tmp = (y * y) * (t_1 + (((x / y) - (x * t)) / y))
    else if (y <= 2.8d+144) then
        tmp = (y * y) * t_1
    else if (y <= 7.2d+282) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * ((t * t) * 0.5);
	double t_2 = x / ((t * (y + ((y * y) * (t * 0.5)))) + 1.0);
	double t_3 = x + (t * ((t * ((x * 0.5) * (y * y))) - (x * y)));
	double tmp;
	if (y <= -8e+241) {
		tmp = t_3;
	} else if (y <= -1.25e+75) {
		tmp = t_2;
	} else if (y <= -2.3e-55) {
		tmp = (2.0 * (x / (a * a))) / (b * b);
	} else if (y <= -2.5e-201) {
		tmp = x / ((a * (b + (a * (((a * 0.16666666666666666) * (b * (b * b))) + (0.5 * (b * b)))))) + 1.0);
	} else if (y <= 1.55e-133) {
		tmp = x + (b * ((b * (x * (0.5 * (a * a)))) - (x * a)));
	} else if (y <= 0.00019) {
		tmp = (y * y) * (t_1 + (((x / y) - (x * t)) / y));
	} else if (y <= 2.8e+144) {
		tmp = (y * y) * t_1;
	} else if (y <= 7.2e+282) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * ((t * t) * 0.5)
	t_2 = x / ((t * (y + ((y * y) * (t * 0.5)))) + 1.0)
	t_3 = x + (t * ((t * ((x * 0.5) * (y * y))) - (x * y)))
	tmp = 0
	if y <= -8e+241:
		tmp = t_3
	elif y <= -1.25e+75:
		tmp = t_2
	elif y <= -2.3e-55:
		tmp = (2.0 * (x / (a * a))) / (b * b)
	elif y <= -2.5e-201:
		tmp = x / ((a * (b + (a * (((a * 0.16666666666666666) * (b * (b * b))) + (0.5 * (b * b)))))) + 1.0)
	elif y <= 1.55e-133:
		tmp = x + (b * ((b * (x * (0.5 * (a * a)))) - (x * a)))
	elif y <= 0.00019:
		tmp = (y * y) * (t_1 + (((x / y) - (x * t)) / y))
	elif y <= 2.8e+144:
		tmp = (y * y) * t_1
	elif y <= 7.2e+282:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * Float64(Float64(t * t) * 0.5))
	t_2 = Float64(x / Float64(Float64(t * Float64(y + Float64(Float64(y * y) * Float64(t * 0.5)))) + 1.0))
	t_3 = Float64(x + Float64(t * Float64(Float64(t * Float64(Float64(x * 0.5) * Float64(y * y))) - Float64(x * y))))
	tmp = 0.0
	if (y <= -8e+241)
		tmp = t_3;
	elseif (y <= -1.25e+75)
		tmp = t_2;
	elseif (y <= -2.3e-55)
		tmp = Float64(Float64(2.0 * Float64(x / Float64(a * a))) / Float64(b * b));
	elseif (y <= -2.5e-201)
		tmp = Float64(x / Float64(Float64(a * Float64(b + Float64(a * Float64(Float64(Float64(a * 0.16666666666666666) * Float64(b * Float64(b * b))) + Float64(0.5 * Float64(b * b)))))) + 1.0));
	elseif (y <= 1.55e-133)
		tmp = Float64(x + Float64(b * Float64(Float64(b * Float64(x * Float64(0.5 * Float64(a * a)))) - Float64(x * a))));
	elseif (y <= 0.00019)
		tmp = Float64(Float64(y * y) * Float64(t_1 + Float64(Float64(Float64(x / y) - Float64(x * t)) / y)));
	elseif (y <= 2.8e+144)
		tmp = Float64(Float64(y * y) * t_1);
	elseif (y <= 7.2e+282)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * ((t * t) * 0.5);
	t_2 = x / ((t * (y + ((y * y) * (t * 0.5)))) + 1.0);
	t_3 = x + (t * ((t * ((x * 0.5) * (y * y))) - (x * y)));
	tmp = 0.0;
	if (y <= -8e+241)
		tmp = t_3;
	elseif (y <= -1.25e+75)
		tmp = t_2;
	elseif (y <= -2.3e-55)
		tmp = (2.0 * (x / (a * a))) / (b * b);
	elseif (y <= -2.5e-201)
		tmp = x / ((a * (b + (a * (((a * 0.16666666666666666) * (b * (b * b))) + (0.5 * (b * b)))))) + 1.0);
	elseif (y <= 1.55e-133)
		tmp = x + (b * ((b * (x * (0.5 * (a * a)))) - (x * a)));
	elseif (y <= 0.00019)
		tmp = (y * y) * (t_1 + (((x / y) - (x * t)) / y));
	elseif (y <= 2.8e+144)
		tmp = (y * y) * t_1;
	elseif (y <= 7.2e+282)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[(N[(t * t), $MachinePrecision] * 0.5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(N[(t * N[(y + N[(N[(y * y), $MachinePrecision] * N[(t * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(t * N[(N[(t * N[(N[(x * 0.5), $MachinePrecision] * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8e+241], t$95$3, If[LessEqual[y, -1.25e+75], t$95$2, If[LessEqual[y, -2.3e-55], N[(N[(2.0 * N[(x / N[(a * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(b * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.5e-201], N[(x / N[(N[(a * N[(b + N[(a * N[(N[(N[(a * 0.16666666666666666), $MachinePrecision] * N[(b * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(0.5 * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.55e-133], N[(x + N[(b * N[(N[(b * N[(x * N[(0.5 * N[(a * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 0.00019], N[(N[(y * y), $MachinePrecision] * N[(t$95$1 + N[(N[(N[(x / y), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.8e+144], N[(N[(y * y), $MachinePrecision] * t$95$1), $MachinePrecision], If[LessEqual[y, 7.2e+282], t$95$2, t$95$3]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y < -8.0000000000000004e241 or 7.19999999999999972e282 < y

   1. Initial program 100.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(t \cdot y\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\left(y \cdot t\right)\right)\right) \]

      2. *-lowering-*.f64 61.7%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, t\right)\right)\right) \]

   7. Simplified 61.7%

      \[\leadsto \frac{x}{e^{\color{blue}{y \cdot t}}} \]

   8. Taylor expanded in t around 0

      \[\leadsto \color{blue}{x + t \cdot \left(-1 \cdot \left(t \cdot \left(-1 \cdot \left(x \cdot {y}^{2}\right) + \frac{1}{2} \cdot \left(x \cdot {y}^{2}\right)\right)\right) - x \cdot y\right)} \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(t \cdot \left(-1 \cdot \left(t \cdot \left(-1 \cdot \left(x \cdot {y}^{2}\right) + \frac{1}{2} \cdot \left(x \cdot {y}^{2}\right)\right)\right) - x \cdot y\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(t, \color{blue}{\left(-1 \cdot \left(t \cdot \left(-1 \cdot \left(x \cdot {y}^{2}\right) + \frac{1}{2} \cdot \left(x \cdot {y}^{2}\right)\right)\right) - x \cdot y\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(-1 \cdot \left(t \cdot \left(-1 \cdot \left(x \cdot {y}^{2}\right) + \frac{1}{2} \cdot \left(x \cdot {y}^{2}\right)\right)\right)\right), \color{blue}{\left(x \cdot y\right)}\right)\right)\right) \]

   10. Simplified 69.8%

       \[\leadsto \color{blue}{x + t \cdot \left(t \cdot \left(\left(0.5 \cdot x\right) \cdot \left(y \cdot y\right)\right) - x \cdot y\right)} \]

   if -8.0000000000000004e241 < y < -1.2500000000000001e75 or 2.80000000000000007e144 < y < 7.19999999999999972e282

   1. Initial program 100.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(t \cdot y\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\left(y \cdot t\right)\right)\right) \]

      2. *-lowering-*.f64 71.7%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, t\right)\right)\right) \]

   7. Simplified 71.7%

      \[\leadsto \frac{x}{e^{\color{blue}{y \cdot t}}} \]

   8. Taylor expanded in t around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + t \cdot \left(y + \frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right)\right)}\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(t \cdot \left(y + \frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \color{blue}{\left(y + \frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right)}\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(y, \color{blue}{\left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right)}\right)\right)\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(y, \left(\left(\frac{1}{2} \cdot t\right) \cdot \color{blue}{{y}^{2}}\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(\left(\frac{1}{2} \cdot t\right), \color{blue}{\left({y}^{2}\right)}\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, t\right), \left({\color{blue}{y}}^{2}\right)\right)\right)\right)\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, t\right), \left(y \cdot \color{blue}{y}\right)\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 71.6%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, t\right), \mathsf{*.f64}\left(y, \color{blue}{y}\right)\right)\right)\right)\right)\right) \]

   10. Simplified 71.6%

       \[\leadsto \frac{x}{\color{blue}{1 + t \cdot \left(y + \left(0.5 \cdot t\right) \cdot \left(y \cdot y\right)\right)}} \]

   if -1.2500000000000001e75 < y < -2.30000000000000011e-55

   1. Initial program 96.6%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 96.6%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(a \cdot b\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 42.4%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, b\right)\right)\right) \]

   7. Simplified 42.4%

      \[\leadsto \frac{x}{e^{\color{blue}{a \cdot b}}} \]

   8. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + b \cdot \left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)\right)}\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(b \cdot \left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \color{blue}{\left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \color{blue}{\left(\frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right)\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(\left(\frac{1}{2} \cdot {a}^{2}\right) \cdot \color{blue}{b}\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\left(\frac{1}{2} \cdot {a}^{2}\right), \color{blue}{b}\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left({a}^{2}\right)\right), b\right)\right)\right)\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left(a \cdot a\right)\right), b\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 22.2%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(a, a\right)\right), b\right)\right)\right)\right)\right) \]

   10. Simplified 22.2%

       \[\leadsto \frac{x}{\color{blue}{1 + b \cdot \left(a + \left(0.5 \cdot \left(a \cdot a\right)\right) \cdot b\right)}} \]
   11. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(b \cdot \color{blue}{\left(\frac{1}{2} \cdot \left(a \cdot a\right)\right)}\right)\right)\right)\right)\right) \]

       2. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(b \cdot \left(\left(\frac{1}{2} \cdot a\right) \cdot \color{blue}{a}\right)\right)\right)\right)\right)\right) \]

       3. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(\left(b \cdot \left(\frac{1}{2} \cdot a\right)\right) \cdot \color{blue}{a}\right)\right)\right)\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\left(b \cdot \left(\frac{1}{2} \cdot a\right)\right), \color{blue}{a}\right)\right)\right)\right)\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \left(\frac{1}{2} \cdot a\right)\right), a\right)\right)\right)\right)\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \left(a \cdot \frac{1}{2}\right)\right), a\right)\right)\right)\right)\right) \]

       7. *-lowering-*.f64 22.2%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \frac{1}{2}\right)\right), a\right)\right)\right)\right)\right) \]

   12. Applied egg-rr 22.2%

       \[\leadsto \frac{x}{1 + b \cdot \left(a + \color{blue}{\left(b \cdot \left(a \cdot 0.5\right)\right) \cdot a}\right)} \]

   13. Taylor expanded in b around inf

       \[\leadsto \color{blue}{2 \cdot \frac{x}{{a}^{2} \cdot {b}^{2}}} \]
   14. Step-by-step derivation

       1. associate-/r* N/A

          \[\leadsto 2 \cdot \frac{\frac{x}{{a}^{2}}}{\color{blue}{{b}^{2}}} \]

       2. associate-*r/ N/A

          \[\leadsto \frac{2 \cdot \frac{x}{{a}^{2}}}{\color{blue}{{b}^{2}}} \]

       3. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left(2 \cdot \frac{x}{{a}^{2}}\right), \color{blue}{\left({b}^{2}\right)}\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(2, \left(\frac{x}{{a}^{2}}\right)\right), \left({\color{blue}{b}}^{2}\right)\right) \]

       5. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(2, \mathsf{/.f64}\left(x, \left({a}^{2}\right)\right)\right), \left({b}^{2}\right)\right) \]

       6. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(2, \mathsf{/.f64}\left(x, \left(a \cdot a\right)\right)\right), \left({b}^{2}\right)\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(2, \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, a\right)\right)\right), \left({b}^{2}\right)\right) \]

       8. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(2, \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, a\right)\right)\right), \left(b \cdot \color{blue}{b}\right)\right) \]

       9. *-lowering-*.f64 52.7%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(2, \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, a\right)\right)\right), \mathsf{*.f64}\left(b, \color{blue}{b}\right)\right) \]

   15. Simplified 52.7%

       \[\leadsto \color{blue}{\frac{2 \cdot \frac{x}{a \cdot a}}{b \cdot b}} \]

   if -2.30000000000000011e-55 < y < -2.5e-201

   1. Initial program 91.4%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 91.4%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(a \cdot b\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 71.8%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, b\right)\right)\right) \]

   7. Simplified 71.8%

      \[\leadsto \frac{x}{e^{\color{blue}{a \cdot b}}} \]

   8. Taylor expanded in a around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + a \cdot \left(b + a \cdot \left(\frac{1}{6} \cdot \left(a \cdot {b}^{3}\right) + \frac{1}{2} \cdot {b}^{2}\right)\right)\right)}\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(a \cdot \left(b + a \cdot \left(\frac{1}{6} \cdot \left(a \cdot {b}^{3}\right) + \frac{1}{2} \cdot {b}^{2}\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \color{blue}{\left(b + a \cdot \left(\frac{1}{6} \cdot \left(a \cdot {b}^{3}\right) + \frac{1}{2} \cdot {b}^{2}\right)\right)}\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(b, \color{blue}{\left(a \cdot \left(\frac{1}{6} \cdot \left(a \cdot {b}^{3}\right) + \frac{1}{2} \cdot {b}^{2}\right)\right)}\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(b, \mathsf{*.f64}\left(a, \color{blue}{\left(\frac{1}{6} \cdot \left(a \cdot {b}^{3}\right) + \frac{1}{2} \cdot {b}^{2}\right)}\right)\right)\right)\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(\left(\frac{1}{6} \cdot \left(a \cdot {b}^{3}\right)\right), \color{blue}{\left(\frac{1}{2} \cdot {b}^{2}\right)}\right)\right)\right)\right)\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(\left(\left(\frac{1}{6} \cdot a\right) \cdot {b}^{3}\right), \left(\color{blue}{\frac{1}{2}} \cdot {b}^{2}\right)\right)\right)\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\frac{1}{6} \cdot a\right), \left({b}^{3}\right)\right), \left(\color{blue}{\frac{1}{2}} \cdot {b}^{2}\right)\right)\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, a\right), \left({b}^{3}\right)\right), \left(\frac{1}{2} \cdot {b}^{2}\right)\right)\right)\right)\right)\right)\right) \]

      9. cube-mult N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, a\right), \left(b \cdot \left(b \cdot b\right)\right)\right), \left(\frac{1}{2} \cdot {b}^{2}\right)\right)\right)\right)\right)\right)\right) \]

      10. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, a\right), \left(b \cdot {b}^{2}\right)\right), \left(\frac{1}{2} \cdot {b}^{2}\right)\right)\right)\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, a\right), \mathsf{*.f64}\left(b, \left({b}^{2}\right)\right)\right), \left(\frac{1}{2} \cdot {b}^{2}\right)\right)\right)\right)\right)\right)\right) \]

      12. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, a\right), \mathsf{*.f64}\left(b, \left(b \cdot b\right)\right)\right), \left(\frac{1}{2} \cdot {b}^{2}\right)\right)\right)\right)\right)\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, a\right), \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(b, b\right)\right)\right), \left(\frac{1}{2} \cdot {b}^{2}\right)\right)\right)\right)\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, a\right), \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(b, b\right)\right)\right), \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{\left({b}^{2}\right)}\right)\right)\right)\right)\right)\right)\right) \]

      15. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, a\right), \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(b, b\right)\right)\right), \mathsf{*.f64}\left(\frac{1}{2}, \left(b \cdot \color{blue}{b}\right)\right)\right)\right)\right)\right)\right)\right) \]

      16. *-lowering-*.f64 62.0%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(b, \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{6}, a\right), \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(b, b\right)\right)\right), \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(b, \color{blue}{b}\right)\right)\right)\right)\right)\right)\right)\right) \]

   10. Simplified 62.0%

       \[\leadsto \frac{x}{\color{blue}{1 + a \cdot \left(b + a \cdot \left(\left(0.16666666666666666 \cdot a\right) \cdot \left(b \cdot \left(b \cdot b\right)\right) + 0.5 \cdot \left(b \cdot b\right)\right)\right)}} \]

   if -2.5e-201 < y < 1.55000000000000008e-133

   1. Initial program 94.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 94.0%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(a \cdot b\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 89.6%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, b\right)\right)\right) \]

   7. Simplified 89.6%

      \[\leadsto \frac{x}{e^{\color{blue}{a \cdot b}}} \]

   8. Taylor expanded in b around 0

      \[\leadsto \color{blue}{x + b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left({a}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({a}^{2} \cdot x\right)\right)\right) - a \cdot x\right)} \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left({a}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({a}^{2} \cdot x\right)\right)\right) - a \cdot x\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \color{blue}{\left(-1 \cdot \left(b \cdot \left(-1 \cdot \left({a}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({a}^{2} \cdot x\right)\right)\right) - a \cdot x\right)}\right)\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(\left(\mathsf{neg}\left(b \cdot \left(-1 \cdot \left({a}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({a}^{2} \cdot x\right)\right)\right)\right) - \color{blue}{a} \cdot x\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(b \cdot \left(\mathsf{neg}\left(\left(-1 \cdot \left({a}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({a}^{2} \cdot x\right)\right)\right)\right) - \color{blue}{a} \cdot x\right)\right)\right) \]

      5. distribute-rgt-out N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(b \cdot \left(\mathsf{neg}\left(\left({a}^{2} \cdot x\right) \cdot \left(-1 + \frac{1}{2}\right)\right)\right) - a \cdot x\right)\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(b \cdot \left(\mathsf{neg}\left(\left({a}^{2} \cdot x\right) \cdot \frac{-1}{2}\right)\right) - a \cdot x\right)\right)\right) \]

      7. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(b \cdot \left(\left({a}^{2} \cdot x\right) \cdot \left(\mathsf{neg}\left(\frac{-1}{2}\right)\right)\right) - a \cdot x\right)\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(b \cdot \left(\left({a}^{2} \cdot x\right) \cdot \frac{1}{2}\right) - a \cdot x\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(b \cdot \left(\frac{1}{2} \cdot \left({a}^{2} \cdot x\right)\right) - a \cdot x\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(b \cdot \left(\frac{1}{2} \cdot \left({a}^{2} \cdot x\right)\right)\right), \color{blue}{\left(a \cdot x\right)}\right)\right)\right) \]

   10. Simplified 67.1%

       \[\leadsto \color{blue}{x + b \cdot \left(b \cdot \left(\left(0.5 \cdot \left(a \cdot a\right)\right) \cdot x\right) - x \cdot a\right)} \]

   if 1.55000000000000008e-133 < y < 1.9000000000000001e-4

   1. Initial program 96.3%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 96.4%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(t \cdot y\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\left(y \cdot t\right)\right)\right) \]

      2. *-lowering-*.f64 66.3%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, t\right)\right)\right) \]

   7. Simplified 66.3%

      \[\leadsto \frac{x}{e^{\color{blue}{y \cdot t}}} \]

   8. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x + y \cdot \left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) - t \cdot x\right)} \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot \left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) - t \cdot x\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) - t \cdot x\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right)\right), \color{blue}{\left(t \cdot x\right)}\right)\right)\right) \]

   10. Simplified 58.9%

       \[\leadsto \color{blue}{x + y \cdot \left(y \cdot \left(0.5 \cdot \left(x \cdot \left(t \cdot t\right)\right)\right) - x \cdot t\right)} \]

   11. Taylor expanded in y around -inf

       \[\leadsto \color{blue}{{y}^{2} \cdot \left(-1 \cdot \frac{-1 \cdot \frac{x}{y} + t \cdot x}{y} + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)} \]
   12. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left({y}^{2}\right), \color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{x}{y} + t \cdot x}{y} + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)}\right) \]

       2. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(y \cdot y\right), \left(\color{blue}{-1 \cdot \frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}} + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \left(\color{blue}{-1 \cdot \frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}} + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) \]

       4. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right) + \color{blue}{-1 \cdot \frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}}\right)\right) \]

       5. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right) + \left(\mathsf{neg}\left(\frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}\right)\right)\right)\right) \]

       6. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right) - \color{blue}{\frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}}\right)\right) \]

       7. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right), \color{blue}{\left(\frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}\right)}\right)\right) \]

       8. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\left(\left({t}^{2} \cdot x\right) \cdot \frac{1}{2}\right), \left(\frac{\color{blue}{-1 \cdot \frac{x}{y} + t \cdot x}}{y}\right)\right)\right) \]

       9. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\left(\left(x \cdot {t}^{2}\right) \cdot \frac{1}{2}\right), \left(\frac{\color{blue}{-1 \cdot \frac{x}{y}} + t \cdot x}{y}\right)\right)\right) \]

       10. associate-*l* N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\left(x \cdot \left({t}^{2} \cdot \frac{1}{2}\right)\right), \left(\frac{\color{blue}{-1 \cdot \frac{x}{y} + t \cdot x}}{y}\right)\right)\right) \]

       11. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \left({t}^{2} \cdot \frac{1}{2}\right)\right), \left(\frac{\color{blue}{-1 \cdot \frac{x}{y} + t \cdot x}}{y}\right)\right)\right) \]

       12. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\left({t}^{2}\right), \frac{1}{2}\right)\right), \left(\frac{-1 \cdot \frac{x}{y} + \color{blue}{t \cdot x}}{y}\right)\right)\right) \]

       13. unpow2 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\left(t \cdot t\right), \frac{1}{2}\right)\right), \left(\frac{-1 \cdot \frac{x}{y} + \color{blue}{t} \cdot x}{y}\right)\right)\right) \]

       14. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, t\right), \frac{1}{2}\right)\right), \left(\frac{-1 \cdot \frac{x}{y} + \color{blue}{t} \cdot x}{y}\right)\right)\right) \]

       15. /-lowering-/.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, t\right), \frac{1}{2}\right)\right), \mathsf{/.f64}\left(\left(-1 \cdot \frac{x}{y} + t \cdot x\right), \color{blue}{y}\right)\right)\right) \]

   13. Simplified 65.7%

       \[\leadsto \color{blue}{\left(y \cdot y\right) \cdot \left(x \cdot \left(\left(t \cdot t\right) \cdot 0.5\right) - \frac{x \cdot t - \frac{x}{y}}{y}\right)} \]

   if 1.9000000000000001e-4 < y < 2.80000000000000007e144

   1. Initial program 96.7%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 96.7%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(t \cdot y\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\left(y \cdot t\right)\right)\right) \]

      2. *-lowering-*.f64 51.2%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, t\right)\right)\right) \]

   7. Simplified 51.2%

      \[\leadsto \frac{x}{e^{\color{blue}{y \cdot t}}} \]

   8. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x + y \cdot \left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) - t \cdot x\right)} \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot \left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) - t \cdot x\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) - t \cdot x\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right)\right), \color{blue}{\left(t \cdot x\right)}\right)\right)\right) \]

   10. Simplified 22.0%

       \[\leadsto \color{blue}{x + y \cdot \left(y \cdot \left(0.5 \cdot \left(x \cdot \left(t \cdot t\right)\right)\right) - x \cdot t\right)} \]

   11. Taylor expanded in y around -inf

       \[\leadsto \color{blue}{{y}^{2} \cdot \left(-1 \cdot \frac{-1 \cdot \frac{x}{y} + t \cdot x}{y} + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)} \]
   12. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left({y}^{2}\right), \color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{x}{y} + t \cdot x}{y} + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)}\right) \]

       2. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(y \cdot y\right), \left(\color{blue}{-1 \cdot \frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}} + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \left(\color{blue}{-1 \cdot \frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}} + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) \]

       4. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right) + \color{blue}{-1 \cdot \frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}}\right)\right) \]

       5. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right) + \left(\mathsf{neg}\left(\frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}\right)\right)\right)\right) \]

       6. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right) - \color{blue}{\frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}}\right)\right) \]

       7. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right), \color{blue}{\left(\frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}\right)}\right)\right) \]

       8. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\left(\left({t}^{2} \cdot x\right) \cdot \frac{1}{2}\right), \left(\frac{\color{blue}{-1 \cdot \frac{x}{y} + t \cdot x}}{y}\right)\right)\right) \]

       9. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\left(\left(x \cdot {t}^{2}\right) \cdot \frac{1}{2}\right), \left(\frac{\color{blue}{-1 \cdot \frac{x}{y}} + t \cdot x}{y}\right)\right)\right) \]

       10. associate-*l* N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\left(x \cdot \left({t}^{2} \cdot \frac{1}{2}\right)\right), \left(\frac{\color{blue}{-1 \cdot \frac{x}{y} + t \cdot x}}{y}\right)\right)\right) \]

       11. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \left({t}^{2} \cdot \frac{1}{2}\right)\right), \left(\frac{\color{blue}{-1 \cdot \frac{x}{y} + t \cdot x}}{y}\right)\right)\right) \]

       12. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\left({t}^{2}\right), \frac{1}{2}\right)\right), \left(\frac{-1 \cdot \frac{x}{y} + \color{blue}{t \cdot x}}{y}\right)\right)\right) \]

       13. unpow2 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\left(t \cdot t\right), \frac{1}{2}\right)\right), \left(\frac{-1 \cdot \frac{x}{y} + \color{blue}{t} \cdot x}{y}\right)\right)\right) \]

       14. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, t\right), \frac{1}{2}\right)\right), \left(\frac{-1 \cdot \frac{x}{y} + \color{blue}{t} \cdot x}{y}\right)\right)\right) \]

       15. /-lowering-/.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, t\right), \frac{1}{2}\right)\right), \mathsf{/.f64}\left(\left(-1 \cdot \frac{x}{y} + t \cdot x\right), \color{blue}{y}\right)\right)\right) \]

   13. Simplified 28.3%

       \[\leadsto \color{blue}{\left(y \cdot y\right) \cdot \left(x \cdot \left(\left(t \cdot t\right) \cdot 0.5\right) - \frac{x \cdot t - \frac{x}{y}}{y}\right)} \]

   14. Taylor expanded in t around inf

       \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \color{blue}{\left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)}\right) \]
   15. Step-by-step derivation

       1. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \left(\left(\frac{1}{2} \cdot {t}^{2}\right) \cdot \color{blue}{x}\right)\right) \]

       2. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \left(x \cdot \color{blue}{\left(\frac{1}{2} \cdot {t}^{2}\right)}\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{1}{2} \cdot {t}^{2}\right)}\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{\left({t}^{2}\right)}\right)\right)\right) \]

       5. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{2}, \left(t \cdot \color{blue}{t}\right)\right)\right)\right) \]

       6. *-lowering-*.f64 51.0%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(t, \color{blue}{t}\right)\right)\right)\right) \]

   16. Simplified 51.0%

       \[\leadsto \left(y \cdot y\right) \cdot \color{blue}{\left(x \cdot \left(0.5 \cdot \left(t \cdot t\right)\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+241}:\\ \;\;\;\;x + t \cdot \left(t \cdot \left(\left(x \cdot 0.5\right) \cdot \left(y \cdot y\right)\right) - x \cdot y\right)\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{+75}:\\ \;\;\;\;\frac{x}{t \cdot \left(y + \left(y \cdot y\right) \cdot \left(t \cdot 0.5\right)\right) + 1}\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-55}:\\ \;\;\;\;\frac{2 \cdot \frac{x}{a \cdot a}}{b \cdot b}\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-201}:\\ \;\;\;\;\frac{x}{a \cdot \left(b + a \cdot \left(\left(a \cdot 0.16666666666666666\right) \cdot \left(b \cdot \left(b \cdot b\right)\right) + 0.5 \cdot \left(b \cdot b\right)\right)\right) + 1}\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-133}:\\ \;\;\;\;x + b \cdot \left(b \cdot \left(x \cdot \left(0.5 \cdot \left(a \cdot a\right)\right)\right) - x \cdot a\right)\\ \mathbf{elif}\;y \leq 0.00019:\\ \;\;\;\;\left(y \cdot y\right) \cdot \left(x \cdot \left(\left(t \cdot t\right) \cdot 0.5\right) + \frac{\frac{x}{y} - x \cdot t}{y}\right)\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+144}:\\ \;\;\;\;\left(y \cdot y\right) \cdot \left(x \cdot \left(\left(t \cdot t\right) \cdot 0.5\right)\right)\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+282}:\\ \;\;\;\;\frac{x}{t \cdot \left(y + \left(y \cdot y\right) \cdot \left(t \cdot 0.5\right)\right) + 1}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \left(t \cdot \left(\left(x \cdot 0.5\right) \cdot \left(y \cdot y\right)\right) - x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 48.4% accurate, 5.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(\left(t \cdot t\right) \cdot 0.5\right)\\ t_2 := 0.5 \cdot \left(a \cdot a\right)\\ t_3 := \frac{x}{t \cdot \left(y + \left(y \cdot y\right) \cdot \left(t \cdot 0.5\right)\right) + 1}\\ t_4 := x + t \cdot \left(t \cdot \left(\left(x \cdot 0.5\right) \cdot \left(y \cdot y\right)\right) - x \cdot y\right)\\ \mathbf{if}\;y \leq -8.5 \cdot 10^{+241}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{+75}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-55}:\\ \;\;\;\;\frac{2 \cdot \frac{x}{a \cdot a}}{b \cdot b}\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-201}:\\ \;\;\;\;\frac{x}{b \cdot \left(a + b \cdot t\_2\right) + 1}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-133}:\\ \;\;\;\;x + b \cdot \left(b \cdot \left(x \cdot t\_2\right) - x \cdot a\right)\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-7}:\\ \;\;\;\;\left(y \cdot y\right) \cdot \left(t\_1 + \frac{\frac{x}{y} - x \cdot t}{y}\right)\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+145}:\\ \;\;\;\;\left(y \cdot y\right) \cdot t\_1\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+282}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (* (* t t) 0.5)))
        (t_2 (* 0.5 (* a a)))
        (t_3 (/ x (+ (* t (+ y (* (* y y) (* t 0.5)))) 1.0)))
        (t_4 (+ x (* t (- (* t (* (* x 0.5) (* y y))) (* x y))))))
   (if (<= y -8.5e+241)
     t_4
     (if (<= y -2.2e+75)
       t_3
       (if (<= y -1.9e-55)
         (/ (* 2.0 (/ x (* a a))) (* b b))
         (if (<= y -6.5e-201)
           (/ x (+ (* b (+ a (* b t_2))) 1.0))
           (if (<= y 1.9e-133)
             (+ x (* b (- (* b (* x t_2)) (* x a))))
             (if (<= y 2.8e-7)
               (* (* y y) (+ t_1 (/ (- (/ x y) (* x t)) y)))
               (if (<= y 9.5e+145)
                 (* (* y y) t_1)
                 (if (<= y 5e+282) t_3 t_4))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * ((t * t) * 0.5);
	double t_2 = 0.5 * (a * a);
	double t_3 = x / ((t * (y + ((y * y) * (t * 0.5)))) + 1.0);
	double t_4 = x + (t * ((t * ((x * 0.5) * (y * y))) - (x * y)));
	double tmp;
	if (y <= -8.5e+241) {
		tmp = t_4;
	} else if (y <= -2.2e+75) {
		tmp = t_3;
	} else if (y <= -1.9e-55) {
		tmp = (2.0 * (x / (a * a))) / (b * b);
	} else if (y <= -6.5e-201) {
		tmp = x / ((b * (a + (b * t_2))) + 1.0);
	} else if (y <= 1.9e-133) {
		tmp = x + (b * ((b * (x * t_2)) - (x * a)));
	} else if (y <= 2.8e-7) {
		tmp = (y * y) * (t_1 + (((x / y) - (x * t)) / y));
	} else if (y <= 9.5e+145) {
		tmp = (y * y) * t_1;
	} else if (y <= 5e+282) {
		tmp = t_3;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = x * ((t * t) * 0.5d0)
    t_2 = 0.5d0 * (a * a)
    t_3 = x / ((t * (y + ((y * y) * (t * 0.5d0)))) + 1.0d0)
    t_4 = x + (t * ((t * ((x * 0.5d0) * (y * y))) - (x * y)))
    if (y <= (-8.5d+241)) then
        tmp = t_4
    else if (y <= (-2.2d+75)) then
        tmp = t_3
    else if (y <= (-1.9d-55)) then
        tmp = (2.0d0 * (x / (a * a))) / (b * b)
    else if (y <= (-6.5d-201)) then
        tmp = x / ((b * (a + (b * t_2))) + 1.0d0)
    else if (y <= 1.9d-133) then
        tmp = x + (b * ((b * (x * t_2)) - (x * a)))
    else if (y <= 2.8d-7) then
        tmp = (y * y) * (t_1 + (((x / y) - (x * t)) / y))
    else if (y <= 9.5d+145) then
        tmp = (y * y) * t_1
    else if (y <= 5d+282) then
        tmp = t_3
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * ((t * t) * 0.5);
	double t_2 = 0.5 * (a * a);
	double t_3 = x / ((t * (y + ((y * y) * (t * 0.5)))) + 1.0);
	double t_4 = x + (t * ((t * ((x * 0.5) * (y * y))) - (x * y)));
	double tmp;
	if (y <= -8.5e+241) {
		tmp = t_4;
	} else if (y <= -2.2e+75) {
		tmp = t_3;
	} else if (y <= -1.9e-55) {
		tmp = (2.0 * (x / (a * a))) / (b * b);
	} else if (y <= -6.5e-201) {
		tmp = x / ((b * (a + (b * t_2))) + 1.0);
	} else if (y <= 1.9e-133) {
		tmp = x + (b * ((b * (x * t_2)) - (x * a)));
	} else if (y <= 2.8e-7) {
		tmp = (y * y) * (t_1 + (((x / y) - (x * t)) / y));
	} else if (y <= 9.5e+145) {
		tmp = (y * y) * t_1;
	} else if (y <= 5e+282) {
		tmp = t_3;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * ((t * t) * 0.5)
	t_2 = 0.5 * (a * a)
	t_3 = x / ((t * (y + ((y * y) * (t * 0.5)))) + 1.0)
	t_4 = x + (t * ((t * ((x * 0.5) * (y * y))) - (x * y)))
	tmp = 0
	if y <= -8.5e+241:
		tmp = t_4
	elif y <= -2.2e+75:
		tmp = t_3
	elif y <= -1.9e-55:
		tmp = (2.0 * (x / (a * a))) / (b * b)
	elif y <= -6.5e-201:
		tmp = x / ((b * (a + (b * t_2))) + 1.0)
	elif y <= 1.9e-133:
		tmp = x + (b * ((b * (x * t_2)) - (x * a)))
	elif y <= 2.8e-7:
		tmp = (y * y) * (t_1 + (((x / y) - (x * t)) / y))
	elif y <= 9.5e+145:
		tmp = (y * y) * t_1
	elif y <= 5e+282:
		tmp = t_3
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * Float64(Float64(t * t) * 0.5))
	t_2 = Float64(0.5 * Float64(a * a))
	t_3 = Float64(x / Float64(Float64(t * Float64(y + Float64(Float64(y * y) * Float64(t * 0.5)))) + 1.0))
	t_4 = Float64(x + Float64(t * Float64(Float64(t * Float64(Float64(x * 0.5) * Float64(y * y))) - Float64(x * y))))
	tmp = 0.0
	if (y <= -8.5e+241)
		tmp = t_4;
	elseif (y <= -2.2e+75)
		tmp = t_3;
	elseif (y <= -1.9e-55)
		tmp = Float64(Float64(2.0 * Float64(x / Float64(a * a))) / Float64(b * b));
	elseif (y <= -6.5e-201)
		tmp = Float64(x / Float64(Float64(b * Float64(a + Float64(b * t_2))) + 1.0));
	elseif (y <= 1.9e-133)
		tmp = Float64(x + Float64(b * Float64(Float64(b * Float64(x * t_2)) - Float64(x * a))));
	elseif (y <= 2.8e-7)
		tmp = Float64(Float64(y * y) * Float64(t_1 + Float64(Float64(Float64(x / y) - Float64(x * t)) / y)));
	elseif (y <= 9.5e+145)
		tmp = Float64(Float64(y * y) * t_1);
	elseif (y <= 5e+282)
		tmp = t_3;
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * ((t * t) * 0.5);
	t_2 = 0.5 * (a * a);
	t_3 = x / ((t * (y + ((y * y) * (t * 0.5)))) + 1.0);
	t_4 = x + (t * ((t * ((x * 0.5) * (y * y))) - (x * y)));
	tmp = 0.0;
	if (y <= -8.5e+241)
		tmp = t_4;
	elseif (y <= -2.2e+75)
		tmp = t_3;
	elseif (y <= -1.9e-55)
		tmp = (2.0 * (x / (a * a))) / (b * b);
	elseif (y <= -6.5e-201)
		tmp = x / ((b * (a + (b * t_2))) + 1.0);
	elseif (y <= 1.9e-133)
		tmp = x + (b * ((b * (x * t_2)) - (x * a)));
	elseif (y <= 2.8e-7)
		tmp = (y * y) * (t_1 + (((x / y) - (x * t)) / y));
	elseif (y <= 9.5e+145)
		tmp = (y * y) * t_1;
	elseif (y <= 5e+282)
		tmp = t_3;
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[(N[(t * t), $MachinePrecision] * 0.5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(0.5 * N[(a * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x / N[(N[(t * N[(y + N[(N[(y * y), $MachinePrecision] * N[(t * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(x + N[(t * N[(N[(t * N[(N[(x * 0.5), $MachinePrecision] * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8.5e+241], t$95$4, If[LessEqual[y, -2.2e+75], t$95$3, If[LessEqual[y, -1.9e-55], N[(N[(2.0 * N[(x / N[(a * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(b * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -6.5e-201], N[(x / N[(N[(b * N[(a + N[(b * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.9e-133], N[(x + N[(b * N[(N[(b * N[(x * t$95$2), $MachinePrecision]), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.8e-7], N[(N[(y * y), $MachinePrecision] * N[(t$95$1 + N[(N[(N[(x / y), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.5e+145], N[(N[(y * y), $MachinePrecision] * t$95$1), $MachinePrecision], If[LessEqual[y, 5e+282], t$95$3, t$95$4]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y < -8.49999999999999954e241 or 4.99999999999999978e282 < y

   1. Initial program 100.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(t \cdot y\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\left(y \cdot t\right)\right)\right) \]

      2. *-lowering-*.f64 61.7%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, t\right)\right)\right) \]

   7. Simplified 61.7%

      \[\leadsto \frac{x}{e^{\color{blue}{y \cdot t}}} \]

   8. Taylor expanded in t around 0

      \[\leadsto \color{blue}{x + t \cdot \left(-1 \cdot \left(t \cdot \left(-1 \cdot \left(x \cdot {y}^{2}\right) + \frac{1}{2} \cdot \left(x \cdot {y}^{2}\right)\right)\right) - x \cdot y\right)} \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(t \cdot \left(-1 \cdot \left(t \cdot \left(-1 \cdot \left(x \cdot {y}^{2}\right) + \frac{1}{2} \cdot \left(x \cdot {y}^{2}\right)\right)\right) - x \cdot y\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(t, \color{blue}{\left(-1 \cdot \left(t \cdot \left(-1 \cdot \left(x \cdot {y}^{2}\right) + \frac{1}{2} \cdot \left(x \cdot {y}^{2}\right)\right)\right) - x \cdot y\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(-1 \cdot \left(t \cdot \left(-1 \cdot \left(x \cdot {y}^{2}\right) + \frac{1}{2} \cdot \left(x \cdot {y}^{2}\right)\right)\right)\right), \color{blue}{\left(x \cdot y\right)}\right)\right)\right) \]

   10. Simplified 69.8%

       \[\leadsto \color{blue}{x + t \cdot \left(t \cdot \left(\left(0.5 \cdot x\right) \cdot \left(y \cdot y\right)\right) - x \cdot y\right)} \]

   if -8.49999999999999954e241 < y < -2.20000000000000012e75 or 9.49999999999999948e145 < y < 4.99999999999999978e282

   1. Initial program 100.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(t \cdot y\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\left(y \cdot t\right)\right)\right) \]

      2. *-lowering-*.f64 71.7%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, t\right)\right)\right) \]

   7. Simplified 71.7%

      \[\leadsto \frac{x}{e^{\color{blue}{y \cdot t}}} \]

   8. Taylor expanded in t around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + t \cdot \left(y + \frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right)\right)}\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(t \cdot \left(y + \frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \color{blue}{\left(y + \frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right)}\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(y, \color{blue}{\left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right)}\right)\right)\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(y, \left(\left(\frac{1}{2} \cdot t\right) \cdot \color{blue}{{y}^{2}}\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(\left(\frac{1}{2} \cdot t\right), \color{blue}{\left({y}^{2}\right)}\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, t\right), \left({\color{blue}{y}}^{2}\right)\right)\right)\right)\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, t\right), \left(y \cdot \color{blue}{y}\right)\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 71.6%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, t\right), \mathsf{*.f64}\left(y, \color{blue}{y}\right)\right)\right)\right)\right)\right) \]

   10. Simplified 71.6%

       \[\leadsto \frac{x}{\color{blue}{1 + t \cdot \left(y + \left(0.5 \cdot t\right) \cdot \left(y \cdot y\right)\right)}} \]

   if -2.20000000000000012e75 < y < -1.8999999999999998e-55

   1. Initial program 96.6%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 96.6%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(a \cdot b\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 42.4%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, b\right)\right)\right) \]

   7. Simplified 42.4%

      \[\leadsto \frac{x}{e^{\color{blue}{a \cdot b}}} \]

   8. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + b \cdot \left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)\right)}\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(b \cdot \left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \color{blue}{\left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \color{blue}{\left(\frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right)\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(\left(\frac{1}{2} \cdot {a}^{2}\right) \cdot \color{blue}{b}\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\left(\frac{1}{2} \cdot {a}^{2}\right), \color{blue}{b}\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left({a}^{2}\right)\right), b\right)\right)\right)\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left(a \cdot a\right)\right), b\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 22.2%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(a, a\right)\right), b\right)\right)\right)\right)\right) \]

   10. Simplified 22.2%

       \[\leadsto \frac{x}{\color{blue}{1 + b \cdot \left(a + \left(0.5 \cdot \left(a \cdot a\right)\right) \cdot b\right)}} \]
   11. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(b \cdot \color{blue}{\left(\frac{1}{2} \cdot \left(a \cdot a\right)\right)}\right)\right)\right)\right)\right) \]

       2. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(b \cdot \left(\left(\frac{1}{2} \cdot a\right) \cdot \color{blue}{a}\right)\right)\right)\right)\right)\right) \]

       3. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(\left(b \cdot \left(\frac{1}{2} \cdot a\right)\right) \cdot \color{blue}{a}\right)\right)\right)\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\left(b \cdot \left(\frac{1}{2} \cdot a\right)\right), \color{blue}{a}\right)\right)\right)\right)\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \left(\frac{1}{2} \cdot a\right)\right), a\right)\right)\right)\right)\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \left(a \cdot \frac{1}{2}\right)\right), a\right)\right)\right)\right)\right) \]

       7. *-lowering-*.f64 22.2%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \frac{1}{2}\right)\right), a\right)\right)\right)\right)\right) \]

   12. Applied egg-rr 22.2%

       \[\leadsto \frac{x}{1 + b \cdot \left(a + \color{blue}{\left(b \cdot \left(a \cdot 0.5\right)\right) \cdot a}\right)} \]

   13. Taylor expanded in b around inf

       \[\leadsto \color{blue}{2 \cdot \frac{x}{{a}^{2} \cdot {b}^{2}}} \]
   14. Step-by-step derivation

       1. associate-/r* N/A

          \[\leadsto 2 \cdot \frac{\frac{x}{{a}^{2}}}{\color{blue}{{b}^{2}}} \]

       2. associate-*r/ N/A

          \[\leadsto \frac{2 \cdot \frac{x}{{a}^{2}}}{\color{blue}{{b}^{2}}} \]

       3. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left(2 \cdot \frac{x}{{a}^{2}}\right), \color{blue}{\left({b}^{2}\right)}\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(2, \left(\frac{x}{{a}^{2}}\right)\right), \left({\color{blue}{b}}^{2}\right)\right) \]

       5. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(2, \mathsf{/.f64}\left(x, \left({a}^{2}\right)\right)\right), \left({b}^{2}\right)\right) \]

       6. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(2, \mathsf{/.f64}\left(x, \left(a \cdot a\right)\right)\right), \left({b}^{2}\right)\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(2, \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, a\right)\right)\right), \left({b}^{2}\right)\right) \]

       8. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(2, \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, a\right)\right)\right), \left(b \cdot \color{blue}{b}\right)\right) \]

       9. *-lowering-*.f64 52.7%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(2, \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, a\right)\right)\right), \mathsf{*.f64}\left(b, \color{blue}{b}\right)\right) \]

   15. Simplified 52.7%

       \[\leadsto \color{blue}{\frac{2 \cdot \frac{x}{a \cdot a}}{b \cdot b}} \]

   if -1.8999999999999998e-55 < y < -6.49999999999999974e-201

   1. Initial program 91.4%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 91.4%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(a \cdot b\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 71.8%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, b\right)\right)\right) \]

   7. Simplified 71.8%

      \[\leadsto \frac{x}{e^{\color{blue}{a \cdot b}}} \]

   8. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + b \cdot \left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)\right)}\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(b \cdot \left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \color{blue}{\left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \color{blue}{\left(\frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right)\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(\left(\frac{1}{2} \cdot {a}^{2}\right) \cdot \color{blue}{b}\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\left(\frac{1}{2} \cdot {a}^{2}\right), \color{blue}{b}\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left({a}^{2}\right)\right), b\right)\right)\right)\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left(a \cdot a\right)\right), b\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 60.1%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(a, a\right)\right), b\right)\right)\right)\right)\right) \]

   10. Simplified 60.1%

       \[\leadsto \frac{x}{\color{blue}{1 + b \cdot \left(a + \left(0.5 \cdot \left(a \cdot a\right)\right) \cdot b\right)}} \]

   if -6.49999999999999974e-201 < y < 1.9000000000000002e-133

   1. Initial program 94.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 94.0%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(a \cdot b\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 89.6%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, b\right)\right)\right) \]

   7. Simplified 89.6%

      \[\leadsto \frac{x}{e^{\color{blue}{a \cdot b}}} \]

   8. Taylor expanded in b around 0

      \[\leadsto \color{blue}{x + b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left({a}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({a}^{2} \cdot x\right)\right)\right) - a \cdot x\right)} \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left({a}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({a}^{2} \cdot x\right)\right)\right) - a \cdot x\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \color{blue}{\left(-1 \cdot \left(b \cdot \left(-1 \cdot \left({a}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({a}^{2} \cdot x\right)\right)\right) - a \cdot x\right)}\right)\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(\left(\mathsf{neg}\left(b \cdot \left(-1 \cdot \left({a}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({a}^{2} \cdot x\right)\right)\right)\right) - \color{blue}{a} \cdot x\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(b \cdot \left(\mathsf{neg}\left(\left(-1 \cdot \left({a}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({a}^{2} \cdot x\right)\right)\right)\right) - \color{blue}{a} \cdot x\right)\right)\right) \]

      5. distribute-rgt-out N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(b \cdot \left(\mathsf{neg}\left(\left({a}^{2} \cdot x\right) \cdot \left(-1 + \frac{1}{2}\right)\right)\right) - a \cdot x\right)\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(b \cdot \left(\mathsf{neg}\left(\left({a}^{2} \cdot x\right) \cdot \frac{-1}{2}\right)\right) - a \cdot x\right)\right)\right) \]

      7. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(b \cdot \left(\left({a}^{2} \cdot x\right) \cdot \left(\mathsf{neg}\left(\frac{-1}{2}\right)\right)\right) - a \cdot x\right)\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(b \cdot \left(\left({a}^{2} \cdot x\right) \cdot \frac{1}{2}\right) - a \cdot x\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(b \cdot \left(\frac{1}{2} \cdot \left({a}^{2} \cdot x\right)\right) - a \cdot x\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(b \cdot \left(\frac{1}{2} \cdot \left({a}^{2} \cdot x\right)\right)\right), \color{blue}{\left(a \cdot x\right)}\right)\right)\right) \]

   10. Simplified 67.1%

       \[\leadsto \color{blue}{x + b \cdot \left(b \cdot \left(\left(0.5 \cdot \left(a \cdot a\right)\right) \cdot x\right) - x \cdot a\right)} \]

   if 1.9000000000000002e-133 < y < 2.80000000000000019e-7

   1. Initial program 96.3%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 96.4%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(t \cdot y\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\left(y \cdot t\right)\right)\right) \]

      2. *-lowering-*.f64 66.3%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, t\right)\right)\right) \]

   7. Simplified 66.3%

      \[\leadsto \frac{x}{e^{\color{blue}{y \cdot t}}} \]

   8. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x + y \cdot \left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) - t \cdot x\right)} \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot \left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) - t \cdot x\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) - t \cdot x\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right)\right), \color{blue}{\left(t \cdot x\right)}\right)\right)\right) \]

   10. Simplified 58.9%

       \[\leadsto \color{blue}{x + y \cdot \left(y \cdot \left(0.5 \cdot \left(x \cdot \left(t \cdot t\right)\right)\right) - x \cdot t\right)} \]

   11. Taylor expanded in y around -inf

       \[\leadsto \color{blue}{{y}^{2} \cdot \left(-1 \cdot \frac{-1 \cdot \frac{x}{y} + t \cdot x}{y} + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)} \]
   12. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left({y}^{2}\right), \color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{x}{y} + t \cdot x}{y} + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)}\right) \]

       2. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(y \cdot y\right), \left(\color{blue}{-1 \cdot \frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}} + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \left(\color{blue}{-1 \cdot \frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}} + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) \]

       4. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right) + \color{blue}{-1 \cdot \frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}}\right)\right) \]

       5. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right) + \left(\mathsf{neg}\left(\frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}\right)\right)\right)\right) \]

       6. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right) - \color{blue}{\frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}}\right)\right) \]

       7. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right), \color{blue}{\left(\frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}\right)}\right)\right) \]

       8. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\left(\left({t}^{2} \cdot x\right) \cdot \frac{1}{2}\right), \left(\frac{\color{blue}{-1 \cdot \frac{x}{y} + t \cdot x}}{y}\right)\right)\right) \]

       9. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\left(\left(x \cdot {t}^{2}\right) \cdot \frac{1}{2}\right), \left(\frac{\color{blue}{-1 \cdot \frac{x}{y}} + t \cdot x}{y}\right)\right)\right) \]

       10. associate-*l* N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\left(x \cdot \left({t}^{2} \cdot \frac{1}{2}\right)\right), \left(\frac{\color{blue}{-1 \cdot \frac{x}{y} + t \cdot x}}{y}\right)\right)\right) \]

       11. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \left({t}^{2} \cdot \frac{1}{2}\right)\right), \left(\frac{\color{blue}{-1 \cdot \frac{x}{y} + t \cdot x}}{y}\right)\right)\right) \]

       12. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\left({t}^{2}\right), \frac{1}{2}\right)\right), \left(\frac{-1 \cdot \frac{x}{y} + \color{blue}{t \cdot x}}{y}\right)\right)\right) \]

       13. unpow2 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\left(t \cdot t\right), \frac{1}{2}\right)\right), \left(\frac{-1 \cdot \frac{x}{y} + \color{blue}{t} \cdot x}{y}\right)\right)\right) \]

       14. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, t\right), \frac{1}{2}\right)\right), \left(\frac{-1 \cdot \frac{x}{y} + \color{blue}{t} \cdot x}{y}\right)\right)\right) \]

       15. /-lowering-/.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, t\right), \frac{1}{2}\right)\right), \mathsf{/.f64}\left(\left(-1 \cdot \frac{x}{y} + t \cdot x\right), \color{blue}{y}\right)\right)\right) \]

   13. Simplified 65.7%

       \[\leadsto \color{blue}{\left(y \cdot y\right) \cdot \left(x \cdot \left(\left(t \cdot t\right) \cdot 0.5\right) - \frac{x \cdot t - \frac{x}{y}}{y}\right)} \]

   if 2.80000000000000019e-7 < y < 9.49999999999999948e145

   1. Initial program 96.7%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 96.7%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(t \cdot y\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\left(y \cdot t\right)\right)\right) \]

      2. *-lowering-*.f64 51.2%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, t\right)\right)\right) \]

   7. Simplified 51.2%

      \[\leadsto \frac{x}{e^{\color{blue}{y \cdot t}}} \]

   8. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x + y \cdot \left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) - t \cdot x\right)} \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot \left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) - t \cdot x\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) - t \cdot x\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right)\right), \color{blue}{\left(t \cdot x\right)}\right)\right)\right) \]

   10. Simplified 22.0%

       \[\leadsto \color{blue}{x + y \cdot \left(y \cdot \left(0.5 \cdot \left(x \cdot \left(t \cdot t\right)\right)\right) - x \cdot t\right)} \]

   11. Taylor expanded in y around -inf

       \[\leadsto \color{blue}{{y}^{2} \cdot \left(-1 \cdot \frac{-1 \cdot \frac{x}{y} + t \cdot x}{y} + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)} \]
   12. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left({y}^{2}\right), \color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{x}{y} + t \cdot x}{y} + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)}\right) \]

       2. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(y \cdot y\right), \left(\color{blue}{-1 \cdot \frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}} + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \left(\color{blue}{-1 \cdot \frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}} + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) \]

       4. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right) + \color{blue}{-1 \cdot \frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}}\right)\right) \]

       5. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right) + \left(\mathsf{neg}\left(\frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}\right)\right)\right)\right) \]

       6. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right) - \color{blue}{\frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}}\right)\right) \]

       7. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right), \color{blue}{\left(\frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}\right)}\right)\right) \]

       8. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\left(\left({t}^{2} \cdot x\right) \cdot \frac{1}{2}\right), \left(\frac{\color{blue}{-1 \cdot \frac{x}{y} + t \cdot x}}{y}\right)\right)\right) \]

       9. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\left(\left(x \cdot {t}^{2}\right) \cdot \frac{1}{2}\right), \left(\frac{\color{blue}{-1 \cdot \frac{x}{y}} + t \cdot x}{y}\right)\right)\right) \]

       10. associate-*l* N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\left(x \cdot \left({t}^{2} \cdot \frac{1}{2}\right)\right), \left(\frac{\color{blue}{-1 \cdot \frac{x}{y} + t \cdot x}}{y}\right)\right)\right) \]

       11. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \left({t}^{2} \cdot \frac{1}{2}\right)\right), \left(\frac{\color{blue}{-1 \cdot \frac{x}{y} + t \cdot x}}{y}\right)\right)\right) \]

       12. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\left({t}^{2}\right), \frac{1}{2}\right)\right), \left(\frac{-1 \cdot \frac{x}{y} + \color{blue}{t \cdot x}}{y}\right)\right)\right) \]

       13. unpow2 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\left(t \cdot t\right), \frac{1}{2}\right)\right), \left(\frac{-1 \cdot \frac{x}{y} + \color{blue}{t} \cdot x}{y}\right)\right)\right) \]

       14. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, t\right), \frac{1}{2}\right)\right), \left(\frac{-1 \cdot \frac{x}{y} + \color{blue}{t} \cdot x}{y}\right)\right)\right) \]

       15. /-lowering-/.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, t\right), \frac{1}{2}\right)\right), \mathsf{/.f64}\left(\left(-1 \cdot \frac{x}{y} + t \cdot x\right), \color{blue}{y}\right)\right)\right) \]

   13. Simplified 28.3%

       \[\leadsto \color{blue}{\left(y \cdot y\right) \cdot \left(x \cdot \left(\left(t \cdot t\right) \cdot 0.5\right) - \frac{x \cdot t - \frac{x}{y}}{y}\right)} \]

   14. Taylor expanded in t around inf

       \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \color{blue}{\left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)}\right) \]
   15. Step-by-step derivation

       1. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \left(\left(\frac{1}{2} \cdot {t}^{2}\right) \cdot \color{blue}{x}\right)\right) \]

       2. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \left(x \cdot \color{blue}{\left(\frac{1}{2} \cdot {t}^{2}\right)}\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{1}{2} \cdot {t}^{2}\right)}\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{\left({t}^{2}\right)}\right)\right)\right) \]

       5. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{2}, \left(t \cdot \color{blue}{t}\right)\right)\right)\right) \]

       6. *-lowering-*.f64 51.0%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(t, \color{blue}{t}\right)\right)\right)\right) \]

   16. Simplified 51.0%

       \[\leadsto \left(y \cdot y\right) \cdot \color{blue}{\left(x \cdot \left(0.5 \cdot \left(t \cdot t\right)\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 63.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+241}:\\ \;\;\;\;x + t \cdot \left(t \cdot \left(\left(x \cdot 0.5\right) \cdot \left(y \cdot y\right)\right) - x \cdot y\right)\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{+75}:\\ \;\;\;\;\frac{x}{t \cdot \left(y + \left(y \cdot y\right) \cdot \left(t \cdot 0.5\right)\right) + 1}\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-55}:\\ \;\;\;\;\frac{2 \cdot \frac{x}{a \cdot a}}{b \cdot b}\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-201}:\\ \;\;\;\;\frac{x}{b \cdot \left(a + b \cdot \left(0.5 \cdot \left(a \cdot a\right)\right)\right) + 1}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-133}:\\ \;\;\;\;x + b \cdot \left(b \cdot \left(x \cdot \left(0.5 \cdot \left(a \cdot a\right)\right)\right) - x \cdot a\right)\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-7}:\\ \;\;\;\;\left(y \cdot y\right) \cdot \left(x \cdot \left(\left(t \cdot t\right) \cdot 0.5\right) + \frac{\frac{x}{y} - x \cdot t}{y}\right)\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+145}:\\ \;\;\;\;\left(y \cdot y\right) \cdot \left(x \cdot \left(\left(t \cdot t\right) \cdot 0.5\right)\right)\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+282}:\\ \;\;\;\;\frac{x}{t \cdot \left(y + \left(y \cdot y\right) \cdot \left(t \cdot 0.5\right)\right) + 1}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \left(t \cdot \left(\left(x \cdot 0.5\right) \cdot \left(y \cdot y\right)\right) - x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 48.7% accurate, 5.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.5 \cdot \left(a \cdot a\right)\\ t_2 := \left(t \cdot t\right) \cdot 0.5\\ t_3 := \frac{x}{t \cdot \left(y + \left(y \cdot y\right) \cdot \left(t \cdot 0.5\right)\right) + 1}\\ t_4 := x + t \cdot \left(t \cdot \left(\left(x \cdot 0.5\right) \cdot \left(y \cdot y\right)\right) - x \cdot y\right)\\ \mathbf{if}\;y \leq -8 \cdot 10^{+241}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;y \leq -1 \cdot 10^{+75}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-55}:\\ \;\;\;\;\frac{2 \cdot \frac{x}{a \cdot a}}{b \cdot b}\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-201}:\\ \;\;\;\;\frac{x}{b \cdot \left(a + b \cdot t\_1\right) + 1}\\ \mathbf{elif}\;y \leq 1.66 \cdot 10^{-141}:\\ \;\;\;\;x + b \cdot \left(b \cdot \left(x \cdot t\_1\right) - x \cdot a\right)\\ \mathbf{elif}\;y \leq 0.245:\\ \;\;\;\;x \cdot \left(y \cdot \left(y \cdot t\_2 - t\right) + 1\right)\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+146}:\\ \;\;\;\;\left(y \cdot y\right) \cdot \left(x \cdot t\_2\right)\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+282}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* 0.5 (* a a)))
        (t_2 (* (* t t) 0.5))
        (t_3 (/ x (+ (* t (+ y (* (* y y) (* t 0.5)))) 1.0)))
        (t_4 (+ x (* t (- (* t (* (* x 0.5) (* y y))) (* x y))))))
   (if (<= y -8e+241)
     t_4
     (if (<= y -1e+75)
       t_3
       (if (<= y -2.3e-55)
         (/ (* 2.0 (/ x (* a a))) (* b b))
         (if (<= y -4e-201)
           (/ x (+ (* b (+ a (* b t_1))) 1.0))
           (if (<= y 1.66e-141)
             (+ x (* b (- (* b (* x t_1)) (* x a))))
             (if (<= y 0.245)
               (* x (+ (* y (- (* y t_2) t)) 1.0))
               (if (<= y 3e+146)
                 (* (* y y) (* x t_2))
                 (if (<= y 7.2e+282) t_3 t_4))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 0.5 * (a * a);
	double t_2 = (t * t) * 0.5;
	double t_3 = x / ((t * (y + ((y * y) * (t * 0.5)))) + 1.0);
	double t_4 = x + (t * ((t * ((x * 0.5) * (y * y))) - (x * y)));
	double tmp;
	if (y <= -8e+241) {
		tmp = t_4;
	} else if (y <= -1e+75) {
		tmp = t_3;
	} else if (y <= -2.3e-55) {
		tmp = (2.0 * (x / (a * a))) / (b * b);
	} else if (y <= -4e-201) {
		tmp = x / ((b * (a + (b * t_1))) + 1.0);
	} else if (y <= 1.66e-141) {
		tmp = x + (b * ((b * (x * t_1)) - (x * a)));
	} else if (y <= 0.245) {
		tmp = x * ((y * ((y * t_2) - t)) + 1.0);
	} else if (y <= 3e+146) {
		tmp = (y * y) * (x * t_2);
	} else if (y <= 7.2e+282) {
		tmp = t_3;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = 0.5d0 * (a * a)
    t_2 = (t * t) * 0.5d0
    t_3 = x / ((t * (y + ((y * y) * (t * 0.5d0)))) + 1.0d0)
    t_4 = x + (t * ((t * ((x * 0.5d0) * (y * y))) - (x * y)))
    if (y <= (-8d+241)) then
        tmp = t_4
    else if (y <= (-1d+75)) then
        tmp = t_3
    else if (y <= (-2.3d-55)) then
        tmp = (2.0d0 * (x / (a * a))) / (b * b)
    else if (y <= (-4d-201)) then
        tmp = x / ((b * (a + (b * t_1))) + 1.0d0)
    else if (y <= 1.66d-141) then
        tmp = x + (b * ((b * (x * t_1)) - (x * a)))
    else if (y <= 0.245d0) then
        tmp = x * ((y * ((y * t_2) - t)) + 1.0d0)
    else if (y <= 3d+146) then
        tmp = (y * y) * (x * t_2)
    else if (y <= 7.2d+282) then
        tmp = t_3
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 0.5 * (a * a);
	double t_2 = (t * t) * 0.5;
	double t_3 = x / ((t * (y + ((y * y) * (t * 0.5)))) + 1.0);
	double t_4 = x + (t * ((t * ((x * 0.5) * (y * y))) - (x * y)));
	double tmp;
	if (y <= -8e+241) {
		tmp = t_4;
	} else if (y <= -1e+75) {
		tmp = t_3;
	} else if (y <= -2.3e-55) {
		tmp = (2.0 * (x / (a * a))) / (b * b);
	} else if (y <= -4e-201) {
		tmp = x / ((b * (a + (b * t_1))) + 1.0);
	} else if (y <= 1.66e-141) {
		tmp = x + (b * ((b * (x * t_1)) - (x * a)));
	} else if (y <= 0.245) {
		tmp = x * ((y * ((y * t_2) - t)) + 1.0);
	} else if (y <= 3e+146) {
		tmp = (y * y) * (x * t_2);
	} else if (y <= 7.2e+282) {
		tmp = t_3;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = 0.5 * (a * a)
	t_2 = (t * t) * 0.5
	t_3 = x / ((t * (y + ((y * y) * (t * 0.5)))) + 1.0)
	t_4 = x + (t * ((t * ((x * 0.5) * (y * y))) - (x * y)))
	tmp = 0
	if y <= -8e+241:
		tmp = t_4
	elif y <= -1e+75:
		tmp = t_3
	elif y <= -2.3e-55:
		tmp = (2.0 * (x / (a * a))) / (b * b)
	elif y <= -4e-201:
		tmp = x / ((b * (a + (b * t_1))) + 1.0)
	elif y <= 1.66e-141:
		tmp = x + (b * ((b * (x * t_1)) - (x * a)))
	elif y <= 0.245:
		tmp = x * ((y * ((y * t_2) - t)) + 1.0)
	elif y <= 3e+146:
		tmp = (y * y) * (x * t_2)
	elif y <= 7.2e+282:
		tmp = t_3
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(0.5 * Float64(a * a))
	t_2 = Float64(Float64(t * t) * 0.5)
	t_3 = Float64(x / Float64(Float64(t * Float64(y + Float64(Float64(y * y) * Float64(t * 0.5)))) + 1.0))
	t_4 = Float64(x + Float64(t * Float64(Float64(t * Float64(Float64(x * 0.5) * Float64(y * y))) - Float64(x * y))))
	tmp = 0.0
	if (y <= -8e+241)
		tmp = t_4;
	elseif (y <= -1e+75)
		tmp = t_3;
	elseif (y <= -2.3e-55)
		tmp = Float64(Float64(2.0 * Float64(x / Float64(a * a))) / Float64(b * b));
	elseif (y <= -4e-201)
		tmp = Float64(x / Float64(Float64(b * Float64(a + Float64(b * t_1))) + 1.0));
	elseif (y <= 1.66e-141)
		tmp = Float64(x + Float64(b * Float64(Float64(b * Float64(x * t_1)) - Float64(x * a))));
	elseif (y <= 0.245)
		tmp = Float64(x * Float64(Float64(y * Float64(Float64(y * t_2) - t)) + 1.0));
	elseif (y <= 3e+146)
		tmp = Float64(Float64(y * y) * Float64(x * t_2));
	elseif (y <= 7.2e+282)
		tmp = t_3;
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 0.5 * (a * a);
	t_2 = (t * t) * 0.5;
	t_3 = x / ((t * (y + ((y * y) * (t * 0.5)))) + 1.0);
	t_4 = x + (t * ((t * ((x * 0.5) * (y * y))) - (x * y)));
	tmp = 0.0;
	if (y <= -8e+241)
		tmp = t_4;
	elseif (y <= -1e+75)
		tmp = t_3;
	elseif (y <= -2.3e-55)
		tmp = (2.0 * (x / (a * a))) / (b * b);
	elseif (y <= -4e-201)
		tmp = x / ((b * (a + (b * t_1))) + 1.0);
	elseif (y <= 1.66e-141)
		tmp = x + (b * ((b * (x * t_1)) - (x * a)));
	elseif (y <= 0.245)
		tmp = x * ((y * ((y * t_2) - t)) + 1.0);
	elseif (y <= 3e+146)
		tmp = (y * y) * (x * t_2);
	elseif (y <= 7.2e+282)
		tmp = t_3;
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(0.5 * N[(a * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * t), $MachinePrecision] * 0.5), $MachinePrecision]}, Block[{t$95$3 = N[(x / N[(N[(t * N[(y + N[(N[(y * y), $MachinePrecision] * N[(t * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(x + N[(t * N[(N[(t * N[(N[(x * 0.5), $MachinePrecision] * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8e+241], t$95$4, If[LessEqual[y, -1e+75], t$95$3, If[LessEqual[y, -2.3e-55], N[(N[(2.0 * N[(x / N[(a * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(b * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4e-201], N[(x / N[(N[(b * N[(a + N[(b * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.66e-141], N[(x + N[(b * N[(N[(b * N[(x * t$95$1), $MachinePrecision]), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 0.245], N[(x * N[(N[(y * N[(N[(y * t$95$2), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3e+146], N[(N[(y * y), $MachinePrecision] * N[(x * t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.2e+282], t$95$3, t$95$4]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y < -8.0000000000000004e241 or 7.19999999999999972e282 < y

   1. Initial program 100.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(t \cdot y\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\left(y \cdot t\right)\right)\right) \]

      2. *-lowering-*.f64 61.7%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, t\right)\right)\right) \]

   7. Simplified 61.7%

      \[\leadsto \frac{x}{e^{\color{blue}{y \cdot t}}} \]

   8. Taylor expanded in t around 0

      \[\leadsto \color{blue}{x + t \cdot \left(-1 \cdot \left(t \cdot \left(-1 \cdot \left(x \cdot {y}^{2}\right) + \frac{1}{2} \cdot \left(x \cdot {y}^{2}\right)\right)\right) - x \cdot y\right)} \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(t \cdot \left(-1 \cdot \left(t \cdot \left(-1 \cdot \left(x \cdot {y}^{2}\right) + \frac{1}{2} \cdot \left(x \cdot {y}^{2}\right)\right)\right) - x \cdot y\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(t, \color{blue}{\left(-1 \cdot \left(t \cdot \left(-1 \cdot \left(x \cdot {y}^{2}\right) + \frac{1}{2} \cdot \left(x \cdot {y}^{2}\right)\right)\right) - x \cdot y\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(\left(-1 \cdot \left(t \cdot \left(-1 \cdot \left(x \cdot {y}^{2}\right) + \frac{1}{2} \cdot \left(x \cdot {y}^{2}\right)\right)\right)\right), \color{blue}{\left(x \cdot y\right)}\right)\right)\right) \]

   10. Simplified 69.8%

       \[\leadsto \color{blue}{x + t \cdot \left(t \cdot \left(\left(0.5 \cdot x\right) \cdot \left(y \cdot y\right)\right) - x \cdot y\right)} \]

   if -8.0000000000000004e241 < y < -9.99999999999999927e74 or 3.00000000000000002e146 < y < 7.19999999999999972e282

   1. Initial program 100.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(t \cdot y\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\left(y \cdot t\right)\right)\right) \]

      2. *-lowering-*.f64 71.7%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, t\right)\right)\right) \]

   7. Simplified 71.7%

      \[\leadsto \frac{x}{e^{\color{blue}{y \cdot t}}} \]

   8. Taylor expanded in t around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + t \cdot \left(y + \frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right)\right)}\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(t \cdot \left(y + \frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \color{blue}{\left(y + \frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right)}\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(y, \color{blue}{\left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right)}\right)\right)\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(y, \left(\left(\frac{1}{2} \cdot t\right) \cdot \color{blue}{{y}^{2}}\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(\left(\frac{1}{2} \cdot t\right), \color{blue}{\left({y}^{2}\right)}\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, t\right), \left({\color{blue}{y}}^{2}\right)\right)\right)\right)\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, t\right), \left(y \cdot \color{blue}{y}\right)\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 71.6%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, t\right), \mathsf{*.f64}\left(y, \color{blue}{y}\right)\right)\right)\right)\right)\right) \]

   10. Simplified 71.6%

       \[\leadsto \frac{x}{\color{blue}{1 + t \cdot \left(y + \left(0.5 \cdot t\right) \cdot \left(y \cdot y\right)\right)}} \]

   if -9.99999999999999927e74 < y < -2.30000000000000011e-55

   1. Initial program 96.6%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 96.6%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(a \cdot b\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 42.4%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, b\right)\right)\right) \]

   7. Simplified 42.4%

      \[\leadsto \frac{x}{e^{\color{blue}{a \cdot b}}} \]

   8. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + b \cdot \left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)\right)}\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(b \cdot \left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \color{blue}{\left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \color{blue}{\left(\frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right)\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(\left(\frac{1}{2} \cdot {a}^{2}\right) \cdot \color{blue}{b}\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\left(\frac{1}{2} \cdot {a}^{2}\right), \color{blue}{b}\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left({a}^{2}\right)\right), b\right)\right)\right)\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left(a \cdot a\right)\right), b\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 22.2%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(a, a\right)\right), b\right)\right)\right)\right)\right) \]

   10. Simplified 22.2%

       \[\leadsto \frac{x}{\color{blue}{1 + b \cdot \left(a + \left(0.5 \cdot \left(a \cdot a\right)\right) \cdot b\right)}} \]
   11. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(b \cdot \color{blue}{\left(\frac{1}{2} \cdot \left(a \cdot a\right)\right)}\right)\right)\right)\right)\right) \]

       2. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(b \cdot \left(\left(\frac{1}{2} \cdot a\right) \cdot \color{blue}{a}\right)\right)\right)\right)\right)\right) \]

       3. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(\left(b \cdot \left(\frac{1}{2} \cdot a\right)\right) \cdot \color{blue}{a}\right)\right)\right)\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\left(b \cdot \left(\frac{1}{2} \cdot a\right)\right), \color{blue}{a}\right)\right)\right)\right)\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \left(\frac{1}{2} \cdot a\right)\right), a\right)\right)\right)\right)\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \left(a \cdot \frac{1}{2}\right)\right), a\right)\right)\right)\right)\right) \]

       7. *-lowering-*.f64 22.2%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \frac{1}{2}\right)\right), a\right)\right)\right)\right)\right) \]

   12. Applied egg-rr 22.2%

       \[\leadsto \frac{x}{1 + b \cdot \left(a + \color{blue}{\left(b \cdot \left(a \cdot 0.5\right)\right) \cdot a}\right)} \]

   13. Taylor expanded in b around inf

       \[\leadsto \color{blue}{2 \cdot \frac{x}{{a}^{2} \cdot {b}^{2}}} \]
   14. Step-by-step derivation

       1. associate-/r* N/A

          \[\leadsto 2 \cdot \frac{\frac{x}{{a}^{2}}}{\color{blue}{{b}^{2}}} \]

       2. associate-*r/ N/A

          \[\leadsto \frac{2 \cdot \frac{x}{{a}^{2}}}{\color{blue}{{b}^{2}}} \]

       3. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left(2 \cdot \frac{x}{{a}^{2}}\right), \color{blue}{\left({b}^{2}\right)}\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(2, \left(\frac{x}{{a}^{2}}\right)\right), \left({\color{blue}{b}}^{2}\right)\right) \]

       5. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(2, \mathsf{/.f64}\left(x, \left({a}^{2}\right)\right)\right), \left({b}^{2}\right)\right) \]

       6. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(2, \mathsf{/.f64}\left(x, \left(a \cdot a\right)\right)\right), \left({b}^{2}\right)\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(2, \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, a\right)\right)\right), \left({b}^{2}\right)\right) \]

       8. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(2, \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, a\right)\right)\right), \left(b \cdot \color{blue}{b}\right)\right) \]

       9. *-lowering-*.f64 52.7%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(2, \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, a\right)\right)\right), \mathsf{*.f64}\left(b, \color{blue}{b}\right)\right) \]

   15. Simplified 52.7%

       \[\leadsto \color{blue}{\frac{2 \cdot \frac{x}{a \cdot a}}{b \cdot b}} \]

   if -2.30000000000000011e-55 < y < -3.99999999999999978e-201

   1. Initial program 91.4%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 91.4%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(a \cdot b\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 71.8%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, b\right)\right)\right) \]

   7. Simplified 71.8%

      \[\leadsto \frac{x}{e^{\color{blue}{a \cdot b}}} \]

   8. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + b \cdot \left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)\right)}\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(b \cdot \left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \color{blue}{\left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \color{blue}{\left(\frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right)\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(\left(\frac{1}{2} \cdot {a}^{2}\right) \cdot \color{blue}{b}\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\left(\frac{1}{2} \cdot {a}^{2}\right), \color{blue}{b}\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left({a}^{2}\right)\right), b\right)\right)\right)\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left(a \cdot a\right)\right), b\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 60.1%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(a, a\right)\right), b\right)\right)\right)\right)\right) \]

   10. Simplified 60.1%

       \[\leadsto \frac{x}{\color{blue}{1 + b \cdot \left(a + \left(0.5 \cdot \left(a \cdot a\right)\right) \cdot b\right)}} \]

   if -3.99999999999999978e-201 < y < 1.66e-141

   1. Initial program 93.8%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 93.8%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(a \cdot b\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 89.3%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, b\right)\right)\right) \]

   7. Simplified 89.3%

      \[\leadsto \frac{x}{e^{\color{blue}{a \cdot b}}} \]

   8. Taylor expanded in b around 0

      \[\leadsto \color{blue}{x + b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left({a}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({a}^{2} \cdot x\right)\right)\right) - a \cdot x\right)} \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left({a}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({a}^{2} \cdot x\right)\right)\right) - a \cdot x\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \color{blue}{\left(-1 \cdot \left(b \cdot \left(-1 \cdot \left({a}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({a}^{2} \cdot x\right)\right)\right) - a \cdot x\right)}\right)\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(\left(\mathsf{neg}\left(b \cdot \left(-1 \cdot \left({a}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({a}^{2} \cdot x\right)\right)\right)\right) - \color{blue}{a} \cdot x\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(b \cdot \left(\mathsf{neg}\left(\left(-1 \cdot \left({a}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({a}^{2} \cdot x\right)\right)\right)\right) - \color{blue}{a} \cdot x\right)\right)\right) \]

      5. distribute-rgt-out N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(b \cdot \left(\mathsf{neg}\left(\left({a}^{2} \cdot x\right) \cdot \left(-1 + \frac{1}{2}\right)\right)\right) - a \cdot x\right)\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(b \cdot \left(\mathsf{neg}\left(\left({a}^{2} \cdot x\right) \cdot \frac{-1}{2}\right)\right) - a \cdot x\right)\right)\right) \]

      7. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(b \cdot \left(\left({a}^{2} \cdot x\right) \cdot \left(\mathsf{neg}\left(\frac{-1}{2}\right)\right)\right) - a \cdot x\right)\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(b \cdot \left(\left({a}^{2} \cdot x\right) \cdot \frac{1}{2}\right) - a \cdot x\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(b \cdot \left(\frac{1}{2} \cdot \left({a}^{2} \cdot x\right)\right) - a \cdot x\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(b \cdot \left(\frac{1}{2} \cdot \left({a}^{2} \cdot x\right)\right)\right), \color{blue}{\left(a \cdot x\right)}\right)\right)\right) \]

   10. Simplified 66.0%

       \[\leadsto \color{blue}{x + b \cdot \left(b \cdot \left(\left(0.5 \cdot \left(a \cdot a\right)\right) \cdot x\right) - x \cdot a\right)} \]

   if 1.66e-141 < y < 0.245

   1. Initial program 96.6%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 96.6%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(t \cdot y\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\left(y \cdot t\right)\right)\right) \]

      2. *-lowering-*.f64 68.6%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, t\right)\right)\right) \]

   7. Simplified 68.6%

      \[\leadsto \frac{x}{e^{\color{blue}{y \cdot t}}} \]

   8. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x + y \cdot \left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) - t \cdot x\right)} \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot \left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) - t \cdot x\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) - t \cdot x\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right)\right), \color{blue}{\left(t \cdot x\right)}\right)\right)\right) \]

   10. Simplified 58.5%

       \[\leadsto \color{blue}{x + y \cdot \left(y \cdot \left(0.5 \cdot \left(x \cdot \left(t \cdot t\right)\right)\right) - x \cdot t\right)} \]

   11. Taylor expanded in x around 0

       \[\leadsto \color{blue}{x \cdot \left(1 + y \cdot \left(\frac{1}{2} \cdot \left({t}^{2} \cdot y\right) - t\right)\right)} \]
   12. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + y \cdot \left(\frac{1}{2} \cdot \left({t}^{2} \cdot y\right) - t\right)\right)}\right) \]

       2. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(y \cdot \left(\frac{1}{2} \cdot \left({t}^{2} \cdot y\right) - t\right)\right)}\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{1}{2} \cdot \left({t}^{2} \cdot y\right) - t\right)}\right)\right)\right) \]

       4. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\left(\frac{1}{2} \cdot \left({t}^{2} \cdot y\right)\right), \color{blue}{t}\right)\right)\right)\right) \]

       5. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\left(\left(\frac{1}{2} \cdot {t}^{2}\right) \cdot y\right), t\right)\right)\right)\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\left(\frac{1}{2} \cdot {t}^{2}\right), y\right), t\right)\right)\right)\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left({t}^{2}\right)\right), y\right), t\right)\right)\right)\right) \]

       8. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left(t \cdot t\right)\right), y\right), t\right)\right)\right)\right) \]

       9. *-lowering-*.f64 61.9%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(t, t\right)\right), y\right), t\right)\right)\right)\right) \]

   13. Simplified 61.9%

       \[\leadsto \color{blue}{x \cdot \left(1 + y \cdot \left(\left(0.5 \cdot \left(t \cdot t\right)\right) \cdot y - t\right)\right)} \]

   if 0.245 < y < 3.00000000000000002e146

   1. Initial program 96.7%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 96.7%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(t \cdot y\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\left(y \cdot t\right)\right)\right) \]

      2. *-lowering-*.f64 51.2%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, t\right)\right)\right) \]

   7. Simplified 51.2%

      \[\leadsto \frac{x}{e^{\color{blue}{y \cdot t}}} \]

   8. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x + y \cdot \left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) - t \cdot x\right)} \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot \left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) - t \cdot x\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) - t \cdot x\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right)\right), \color{blue}{\left(t \cdot x\right)}\right)\right)\right) \]

   10. Simplified 22.0%

       \[\leadsto \color{blue}{x + y \cdot \left(y \cdot \left(0.5 \cdot \left(x \cdot \left(t \cdot t\right)\right)\right) - x \cdot t\right)} \]

   11. Taylor expanded in y around -inf

       \[\leadsto \color{blue}{{y}^{2} \cdot \left(-1 \cdot \frac{-1 \cdot \frac{x}{y} + t \cdot x}{y} + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)} \]
   12. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left({y}^{2}\right), \color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{x}{y} + t \cdot x}{y} + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)}\right) \]

       2. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(y \cdot y\right), \left(\color{blue}{-1 \cdot \frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}} + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \left(\color{blue}{-1 \cdot \frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}} + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) \]

       4. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right) + \color{blue}{-1 \cdot \frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}}\right)\right) \]

       5. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right) + \left(\mathsf{neg}\left(\frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}\right)\right)\right)\right) \]

       6. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right) - \color{blue}{\frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}}\right)\right) \]

       7. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right), \color{blue}{\left(\frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}\right)}\right)\right) \]

       8. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\left(\left({t}^{2} \cdot x\right) \cdot \frac{1}{2}\right), \left(\frac{\color{blue}{-1 \cdot \frac{x}{y} + t \cdot x}}{y}\right)\right)\right) \]

       9. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\left(\left(x \cdot {t}^{2}\right) \cdot \frac{1}{2}\right), \left(\frac{\color{blue}{-1 \cdot \frac{x}{y}} + t \cdot x}{y}\right)\right)\right) \]

       10. associate-*l* N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\left(x \cdot \left({t}^{2} \cdot \frac{1}{2}\right)\right), \left(\frac{\color{blue}{-1 \cdot \frac{x}{y} + t \cdot x}}{y}\right)\right)\right) \]

       11. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \left({t}^{2} \cdot \frac{1}{2}\right)\right), \left(\frac{\color{blue}{-1 \cdot \frac{x}{y} + t \cdot x}}{y}\right)\right)\right) \]

       12. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\left({t}^{2}\right), \frac{1}{2}\right)\right), \left(\frac{-1 \cdot \frac{x}{y} + \color{blue}{t \cdot x}}{y}\right)\right)\right) \]

       13. unpow2 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\left(t \cdot t\right), \frac{1}{2}\right)\right), \left(\frac{-1 \cdot \frac{x}{y} + \color{blue}{t} \cdot x}{y}\right)\right)\right) \]

       14. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, t\right), \frac{1}{2}\right)\right), \left(\frac{-1 \cdot \frac{x}{y} + \color{blue}{t} \cdot x}{y}\right)\right)\right) \]

       15. /-lowering-/.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, t\right), \frac{1}{2}\right)\right), \mathsf{/.f64}\left(\left(-1 \cdot \frac{x}{y} + t \cdot x\right), \color{blue}{y}\right)\right)\right) \]

   13. Simplified 28.3%

       \[\leadsto \color{blue}{\left(y \cdot y\right) \cdot \left(x \cdot \left(\left(t \cdot t\right) \cdot 0.5\right) - \frac{x \cdot t - \frac{x}{y}}{y}\right)} \]

   14. Taylor expanded in t around inf

       \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \color{blue}{\left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)}\right) \]
   15. Step-by-step derivation

       1. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \left(\left(\frac{1}{2} \cdot {t}^{2}\right) \cdot \color{blue}{x}\right)\right) \]

       2. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \left(x \cdot \color{blue}{\left(\frac{1}{2} \cdot {t}^{2}\right)}\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{1}{2} \cdot {t}^{2}\right)}\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{\left({t}^{2}\right)}\right)\right)\right) \]

       5. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{2}, \left(t \cdot \color{blue}{t}\right)\right)\right)\right) \]

       6. *-lowering-*.f64 51.0%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(t, \color{blue}{t}\right)\right)\right)\right) \]

   16. Simplified 51.0%

       \[\leadsto \left(y \cdot y\right) \cdot \color{blue}{\left(x \cdot \left(0.5 \cdot \left(t \cdot t\right)\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+241}:\\ \;\;\;\;x + t \cdot \left(t \cdot \left(\left(x \cdot 0.5\right) \cdot \left(y \cdot y\right)\right) - x \cdot y\right)\\ \mathbf{elif}\;y \leq -1 \cdot 10^{+75}:\\ \;\;\;\;\frac{x}{t \cdot \left(y + \left(y \cdot y\right) \cdot \left(t \cdot 0.5\right)\right) + 1}\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-55}:\\ \;\;\;\;\frac{2 \cdot \frac{x}{a \cdot a}}{b \cdot b}\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-201}:\\ \;\;\;\;\frac{x}{b \cdot \left(a + b \cdot \left(0.5 \cdot \left(a \cdot a\right)\right)\right) + 1}\\ \mathbf{elif}\;y \leq 1.66 \cdot 10^{-141}:\\ \;\;\;\;x + b \cdot \left(b \cdot \left(x \cdot \left(0.5 \cdot \left(a \cdot a\right)\right)\right) - x \cdot a\right)\\ \mathbf{elif}\;y \leq 0.245:\\ \;\;\;\;x \cdot \left(y \cdot \left(y \cdot \left(\left(t \cdot t\right) \cdot 0.5\right) - t\right) + 1\right)\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+146}:\\ \;\;\;\;\left(y \cdot y\right) \cdot \left(x \cdot \left(\left(t \cdot t\right) \cdot 0.5\right)\right)\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+282}:\\ \;\;\;\;\frac{x}{t \cdot \left(y + \left(y \cdot y\right) \cdot \left(t \cdot 0.5\right)\right) + 1}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \left(t \cdot \left(\left(x \cdot 0.5\right) \cdot \left(y \cdot y\right)\right) - x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 46.6% accurate, 7.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.5 \cdot \left(a \cdot a\right)\\ \mathbf{if}\;y \leq -8.5 \cdot 10^{+241}:\\ \;\;\;\;\frac{x}{0.5 \cdot \left(a \cdot \left(a \cdot \left(b \cdot b\right)\right)\right)}\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{+69}:\\ \;\;\;\;\frac{x}{t \cdot \left(y + \left(y \cdot y\right) \cdot \left(t \cdot 0.5\right)\right) + 1}\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-55}:\\ \;\;\;\;\frac{2 \cdot \frac{x}{a \cdot a}}{b \cdot b}\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-201}:\\ \;\;\;\;\frac{x}{b \cdot \left(a + b \cdot t\_1\right) + 1}\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{-141}:\\ \;\;\;\;x + b \cdot \left(b \cdot \left(x \cdot t\_1\right) - x \cdot a\right)\\ \mathbf{elif}\;y \leq 0.8:\\ \;\;\;\;x \cdot \left(y \cdot \left(y \cdot \left(\left(t \cdot t\right) \cdot 0.5\right) - t\right) + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(0.5 \cdot \left(y \cdot \left(x \cdot \left(t \cdot t\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* 0.5 (* a a))))
   (if (<= y -8.5e+241)
     (/ x (* 0.5 (* a (* a (* b b)))))
     (if (<= y -5.5e+69)
       (/ x (+ (* t (+ y (* (* y y) (* t 0.5)))) 1.0))
       (if (<= y -2.3e-55)
         (/ (* 2.0 (/ x (* a a))) (* b b))
         (if (<= y -5e-201)
           (/ x (+ (* b (+ a (* b t_1))) 1.0))
           (if (<= y 4.9e-141)
             (+ x (* b (- (* b (* x t_1)) (* x a))))
             (if (<= y 0.8)
               (* x (+ (* y (- (* y (* (* t t) 0.5)) t)) 1.0))
               (* y (* 0.5 (* y (* x (* t t)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 0.5 * (a * a);
	double tmp;
	if (y <= -8.5e+241) {
		tmp = x / (0.5 * (a * (a * (b * b))));
	} else if (y <= -5.5e+69) {
		tmp = x / ((t * (y + ((y * y) * (t * 0.5)))) + 1.0);
	} else if (y <= -2.3e-55) {
		tmp = (2.0 * (x / (a * a))) / (b * b);
	} else if (y <= -5e-201) {
		tmp = x / ((b * (a + (b * t_1))) + 1.0);
	} else if (y <= 4.9e-141) {
		tmp = x + (b * ((b * (x * t_1)) - (x * a)));
	} else if (y <= 0.8) {
		tmp = x * ((y * ((y * ((t * t) * 0.5)) - t)) + 1.0);
	} else {
		tmp = y * (0.5 * (y * (x * (t * t))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 0.5d0 * (a * a)
    if (y <= (-8.5d+241)) then
        tmp = x / (0.5d0 * (a * (a * (b * b))))
    else if (y <= (-5.5d+69)) then
        tmp = x / ((t * (y + ((y * y) * (t * 0.5d0)))) + 1.0d0)
    else if (y <= (-2.3d-55)) then
        tmp = (2.0d0 * (x / (a * a))) / (b * b)
    else if (y <= (-5d-201)) then
        tmp = x / ((b * (a + (b * t_1))) + 1.0d0)
    else if (y <= 4.9d-141) then
        tmp = x + (b * ((b * (x * t_1)) - (x * a)))
    else if (y <= 0.8d0) then
        tmp = x * ((y * ((y * ((t * t) * 0.5d0)) - t)) + 1.0d0)
    else
        tmp = y * (0.5d0 * (y * (x * (t * t))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 0.5 * (a * a);
	double tmp;
	if (y <= -8.5e+241) {
		tmp = x / (0.5 * (a * (a * (b * b))));
	} else if (y <= -5.5e+69) {
		tmp = x / ((t * (y + ((y * y) * (t * 0.5)))) + 1.0);
	} else if (y <= -2.3e-55) {
		tmp = (2.0 * (x / (a * a))) / (b * b);
	} else if (y <= -5e-201) {
		tmp = x / ((b * (a + (b * t_1))) + 1.0);
	} else if (y <= 4.9e-141) {
		tmp = x + (b * ((b * (x * t_1)) - (x * a)));
	} else if (y <= 0.8) {
		tmp = x * ((y * ((y * ((t * t) * 0.5)) - t)) + 1.0);
	} else {
		tmp = y * (0.5 * (y * (x * (t * t))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = 0.5 * (a * a)
	tmp = 0
	if y <= -8.5e+241:
		tmp = x / (0.5 * (a * (a * (b * b))))
	elif y <= -5.5e+69:
		tmp = x / ((t * (y + ((y * y) * (t * 0.5)))) + 1.0)
	elif y <= -2.3e-55:
		tmp = (2.0 * (x / (a * a))) / (b * b)
	elif y <= -5e-201:
		tmp = x / ((b * (a + (b * t_1))) + 1.0)
	elif y <= 4.9e-141:
		tmp = x + (b * ((b * (x * t_1)) - (x * a)))
	elif y <= 0.8:
		tmp = x * ((y * ((y * ((t * t) * 0.5)) - t)) + 1.0)
	else:
		tmp = y * (0.5 * (y * (x * (t * t))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(0.5 * Float64(a * a))
	tmp = 0.0
	if (y <= -8.5e+241)
		tmp = Float64(x / Float64(0.5 * Float64(a * Float64(a * Float64(b * b)))));
	elseif (y <= -5.5e+69)
		tmp = Float64(x / Float64(Float64(t * Float64(y + Float64(Float64(y * y) * Float64(t * 0.5)))) + 1.0));
	elseif (y <= -2.3e-55)
		tmp = Float64(Float64(2.0 * Float64(x / Float64(a * a))) / Float64(b * b));
	elseif (y <= -5e-201)
		tmp = Float64(x / Float64(Float64(b * Float64(a + Float64(b * t_1))) + 1.0));
	elseif (y <= 4.9e-141)
		tmp = Float64(x + Float64(b * Float64(Float64(b * Float64(x * t_1)) - Float64(x * a))));
	elseif (y <= 0.8)
		tmp = Float64(x * Float64(Float64(y * Float64(Float64(y * Float64(Float64(t * t) * 0.5)) - t)) + 1.0));
	else
		tmp = Float64(y * Float64(0.5 * Float64(y * Float64(x * Float64(t * t)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 0.5 * (a * a);
	tmp = 0.0;
	if (y <= -8.5e+241)
		tmp = x / (0.5 * (a * (a * (b * b))));
	elseif (y <= -5.5e+69)
		tmp = x / ((t * (y + ((y * y) * (t * 0.5)))) + 1.0);
	elseif (y <= -2.3e-55)
		tmp = (2.0 * (x / (a * a))) / (b * b);
	elseif (y <= -5e-201)
		tmp = x / ((b * (a + (b * t_1))) + 1.0);
	elseif (y <= 4.9e-141)
		tmp = x + (b * ((b * (x * t_1)) - (x * a)));
	elseif (y <= 0.8)
		tmp = x * ((y * ((y * ((t * t) * 0.5)) - t)) + 1.0);
	else
		tmp = y * (0.5 * (y * (x * (t * t))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(0.5 * N[(a * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8.5e+241], N[(x / N[(0.5 * N[(a * N[(a * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -5.5e+69], N[(x / N[(N[(t * N[(y + N[(N[(y * y), $MachinePrecision] * N[(t * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.3e-55], N[(N[(2.0 * N[(x / N[(a * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(b * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -5e-201], N[(x / N[(N[(b * N[(a + N[(b * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.9e-141], N[(x + N[(b * N[(N[(b * N[(x * t$95$1), $MachinePrecision]), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 0.8], N[(x * N[(N[(y * N[(N[(y * N[(N[(t * t), $MachinePrecision] * 0.5), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(y * N[(0.5 * N[(y * N[(x * N[(t * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y < -8.49999999999999954e241

   1. Initial program 100.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(a \cdot b\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 14.7%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, b\right)\right)\right) \]

   7. Simplified 14.7%

      \[\leadsto \frac{x}{e^{\color{blue}{a \cdot b}}} \]

   8. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + b \cdot \left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)\right)}\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(b \cdot \left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \color{blue}{\left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \color{blue}{\left(\frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right)\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(\left(\frac{1}{2} \cdot {a}^{2}\right) \cdot \color{blue}{b}\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\left(\frac{1}{2} \cdot {a}^{2}\right), \color{blue}{b}\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left({a}^{2}\right)\right), b\right)\right)\right)\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left(a \cdot a\right)\right), b\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 3.5%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(a, a\right)\right), b\right)\right)\right)\right)\right) \]

   10. Simplified 3.5%

       \[\leadsto \frac{x}{\color{blue}{1 + b \cdot \left(a + \left(0.5 \cdot \left(a \cdot a\right)\right) \cdot b\right)}} \]
   11. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(b \cdot \color{blue}{\left(\frac{1}{2} \cdot \left(a \cdot a\right)\right)}\right)\right)\right)\right)\right) \]

       2. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(b \cdot \left(\left(\frac{1}{2} \cdot a\right) \cdot \color{blue}{a}\right)\right)\right)\right)\right)\right) \]

       3. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(\left(b \cdot \left(\frac{1}{2} \cdot a\right)\right) \cdot \color{blue}{a}\right)\right)\right)\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\left(b \cdot \left(\frac{1}{2} \cdot a\right)\right), \color{blue}{a}\right)\right)\right)\right)\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \left(\frac{1}{2} \cdot a\right)\right), a\right)\right)\right)\right)\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \left(a \cdot \frac{1}{2}\right)\right), a\right)\right)\right)\right)\right) \]

       7. *-lowering-*.f64 3.8%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \frac{1}{2}\right)\right), a\right)\right)\right)\right)\right) \]

   12. Applied egg-rr 3.8%

       \[\leadsto \frac{x}{1 + b \cdot \left(a + \color{blue}{\left(b \cdot \left(a \cdot 0.5\right)\right) \cdot a}\right)} \]

   13. Taylor expanded in b around inf

       \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(\frac{1}{2} \cdot \left({a}^{2} \cdot {b}^{2}\right)\right)}\right) \]
   14. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{\left({a}^{2} \cdot {b}^{2}\right)}\right)\right) \]

       2. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{2}, \left(\left(a \cdot a\right) \cdot {\color{blue}{b}}^{2}\right)\right)\right) \]

       3. associate-*l* N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{2}, \left(a \cdot \color{blue}{\left(a \cdot {b}^{2}\right)}\right)\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(a, \color{blue}{\left(a \cdot {b}^{2}\right)}\right)\right)\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(a, \color{blue}{\left({b}^{2}\right)}\right)\right)\right)\right) \]

       6. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(a, \left(b \cdot \color{blue}{b}\right)\right)\right)\right)\right) \]

       7. *-lowering-*.f64 54.4%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(b, \color{blue}{b}\right)\right)\right)\right)\right) \]

   15. Simplified 54.4%

       \[\leadsto \frac{x}{\color{blue}{0.5 \cdot \left(a \cdot \left(a \cdot \left(b \cdot b\right)\right)\right)}} \]

   if -8.49999999999999954e241 < y < -5.50000000000000002e69

   1. Initial program 100.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(t \cdot y\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\left(y \cdot t\right)\right)\right) \]

      2. *-lowering-*.f64 82.7%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, t\right)\right)\right) \]

   7. Simplified 82.7%

      \[\leadsto \frac{x}{e^{\color{blue}{y \cdot t}}} \]

   8. Taylor expanded in t around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + t \cdot \left(y + \frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right)\right)}\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(t \cdot \left(y + \frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \color{blue}{\left(y + \frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right)}\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(y, \color{blue}{\left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right)}\right)\right)\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(y, \left(\left(\frac{1}{2} \cdot t\right) \cdot \color{blue}{{y}^{2}}\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(\left(\frac{1}{2} \cdot t\right), \color{blue}{\left({y}^{2}\right)}\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, t\right), \left({\color{blue}{y}}^{2}\right)\right)\right)\right)\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, t\right), \left(y \cdot \color{blue}{y}\right)\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 61.8%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, t\right), \mathsf{*.f64}\left(y, \color{blue}{y}\right)\right)\right)\right)\right)\right) \]

   10. Simplified 61.8%

       \[\leadsto \frac{x}{\color{blue}{1 + t \cdot \left(y + \left(0.5 \cdot t\right) \cdot \left(y \cdot y\right)\right)}} \]

   if -5.50000000000000002e69 < y < -2.30000000000000011e-55

   1. Initial program 96.6%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 96.6%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(a \cdot b\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 42.4%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, b\right)\right)\right) \]

   7. Simplified 42.4%

      \[\leadsto \frac{x}{e^{\color{blue}{a \cdot b}}} \]

   8. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + b \cdot \left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)\right)}\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(b \cdot \left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \color{blue}{\left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \color{blue}{\left(\frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right)\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(\left(\frac{1}{2} \cdot {a}^{2}\right) \cdot \color{blue}{b}\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\left(\frac{1}{2} \cdot {a}^{2}\right), \color{blue}{b}\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left({a}^{2}\right)\right), b\right)\right)\right)\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left(a \cdot a\right)\right), b\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 22.2%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(a, a\right)\right), b\right)\right)\right)\right)\right) \]

   10. Simplified 22.2%

       \[\leadsto \frac{x}{\color{blue}{1 + b \cdot \left(a + \left(0.5 \cdot \left(a \cdot a\right)\right) \cdot b\right)}} \]
   11. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(b \cdot \color{blue}{\left(\frac{1}{2} \cdot \left(a \cdot a\right)\right)}\right)\right)\right)\right)\right) \]

       2. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(b \cdot \left(\left(\frac{1}{2} \cdot a\right) \cdot \color{blue}{a}\right)\right)\right)\right)\right)\right) \]

       3. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(\left(b \cdot \left(\frac{1}{2} \cdot a\right)\right) \cdot \color{blue}{a}\right)\right)\right)\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\left(b \cdot \left(\frac{1}{2} \cdot a\right)\right), \color{blue}{a}\right)\right)\right)\right)\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \left(\frac{1}{2} \cdot a\right)\right), a\right)\right)\right)\right)\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \left(a \cdot \frac{1}{2}\right)\right), a\right)\right)\right)\right)\right) \]

       7. *-lowering-*.f64 22.2%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \frac{1}{2}\right)\right), a\right)\right)\right)\right)\right) \]

   12. Applied egg-rr 22.2%

       \[\leadsto \frac{x}{1 + b \cdot \left(a + \color{blue}{\left(b \cdot \left(a \cdot 0.5\right)\right) \cdot a}\right)} \]

   13. Taylor expanded in b around inf

       \[\leadsto \color{blue}{2 \cdot \frac{x}{{a}^{2} \cdot {b}^{2}}} \]
   14. Step-by-step derivation

       1. associate-/r* N/A

          \[\leadsto 2 \cdot \frac{\frac{x}{{a}^{2}}}{\color{blue}{{b}^{2}}} \]

       2. associate-*r/ N/A

          \[\leadsto \frac{2 \cdot \frac{x}{{a}^{2}}}{\color{blue}{{b}^{2}}} \]

       3. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left(2 \cdot \frac{x}{{a}^{2}}\right), \color{blue}{\left({b}^{2}\right)}\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(2, \left(\frac{x}{{a}^{2}}\right)\right), \left({\color{blue}{b}}^{2}\right)\right) \]

       5. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(2, \mathsf{/.f64}\left(x, \left({a}^{2}\right)\right)\right), \left({b}^{2}\right)\right) \]

       6. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(2, \mathsf{/.f64}\left(x, \left(a \cdot a\right)\right)\right), \left({b}^{2}\right)\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(2, \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, a\right)\right)\right), \left({b}^{2}\right)\right) \]

       8. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(2, \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, a\right)\right)\right), \left(b \cdot \color{blue}{b}\right)\right) \]

       9. *-lowering-*.f64 52.7%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(2, \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, a\right)\right)\right), \mathsf{*.f64}\left(b, \color{blue}{b}\right)\right) \]

   15. Simplified 52.7%

       \[\leadsto \color{blue}{\frac{2 \cdot \frac{x}{a \cdot a}}{b \cdot b}} \]

   if -2.30000000000000011e-55 < y < -4.9999999999999999e-201

   1. Initial program 91.4%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 91.4%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(a \cdot b\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 71.8%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, b\right)\right)\right) \]

   7. Simplified 71.8%

      \[\leadsto \frac{x}{e^{\color{blue}{a \cdot b}}} \]

   8. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + b \cdot \left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)\right)}\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(b \cdot \left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \color{blue}{\left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \color{blue}{\left(\frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right)\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(\left(\frac{1}{2} \cdot {a}^{2}\right) \cdot \color{blue}{b}\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\left(\frac{1}{2} \cdot {a}^{2}\right), \color{blue}{b}\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left({a}^{2}\right)\right), b\right)\right)\right)\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left(a \cdot a\right)\right), b\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 60.1%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(a, a\right)\right), b\right)\right)\right)\right)\right) \]

   10. Simplified 60.1%

       \[\leadsto \frac{x}{\color{blue}{1 + b \cdot \left(a + \left(0.5 \cdot \left(a \cdot a\right)\right) \cdot b\right)}} \]

   if -4.9999999999999999e-201 < y < 4.90000000000000006e-141

   1. Initial program 93.8%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 93.8%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(a \cdot b\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 89.3%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, b\right)\right)\right) \]

   7. Simplified 89.3%

      \[\leadsto \frac{x}{e^{\color{blue}{a \cdot b}}} \]

   8. Taylor expanded in b around 0

      \[\leadsto \color{blue}{x + b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left({a}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({a}^{2} \cdot x\right)\right)\right) - a \cdot x\right)} \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left({a}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({a}^{2} \cdot x\right)\right)\right) - a \cdot x\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \color{blue}{\left(-1 \cdot \left(b \cdot \left(-1 \cdot \left({a}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({a}^{2} \cdot x\right)\right)\right) - a \cdot x\right)}\right)\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(\left(\mathsf{neg}\left(b \cdot \left(-1 \cdot \left({a}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({a}^{2} \cdot x\right)\right)\right)\right) - \color{blue}{a} \cdot x\right)\right)\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(b \cdot \left(\mathsf{neg}\left(\left(-1 \cdot \left({a}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({a}^{2} \cdot x\right)\right)\right)\right) - \color{blue}{a} \cdot x\right)\right)\right) \]

      5. distribute-rgt-out N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(b \cdot \left(\mathsf{neg}\left(\left({a}^{2} \cdot x\right) \cdot \left(-1 + \frac{1}{2}\right)\right)\right) - a \cdot x\right)\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(b \cdot \left(\mathsf{neg}\left(\left({a}^{2} \cdot x\right) \cdot \frac{-1}{2}\right)\right) - a \cdot x\right)\right)\right) \]

      7. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(b \cdot \left(\left({a}^{2} \cdot x\right) \cdot \left(\mathsf{neg}\left(\frac{-1}{2}\right)\right)\right) - a \cdot x\right)\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(b \cdot \left(\left({a}^{2} \cdot x\right) \cdot \frac{1}{2}\right) - a \cdot x\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(b \cdot \left(\frac{1}{2} \cdot \left({a}^{2} \cdot x\right)\right) - a \cdot x\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(b \cdot \left(\frac{1}{2} \cdot \left({a}^{2} \cdot x\right)\right)\right), \color{blue}{\left(a \cdot x\right)}\right)\right)\right) \]

   10. Simplified 66.0%

       \[\leadsto \color{blue}{x + b \cdot \left(b \cdot \left(\left(0.5 \cdot \left(a \cdot a\right)\right) \cdot x\right) - x \cdot a\right)} \]

   if 4.90000000000000006e-141 < y < 0.80000000000000004

   1. Initial program 96.6%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 96.6%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(t \cdot y\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\left(y \cdot t\right)\right)\right) \]

      2. *-lowering-*.f64 68.6%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, t\right)\right)\right) \]

   7. Simplified 68.6%

      \[\leadsto \frac{x}{e^{\color{blue}{y \cdot t}}} \]

   8. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x + y \cdot \left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) - t \cdot x\right)} \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot \left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) - t \cdot x\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) - t \cdot x\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right)\right), \color{blue}{\left(t \cdot x\right)}\right)\right)\right) \]

   10. Simplified 58.5%

       \[\leadsto \color{blue}{x + y \cdot \left(y \cdot \left(0.5 \cdot \left(x \cdot \left(t \cdot t\right)\right)\right) - x \cdot t\right)} \]

   11. Taylor expanded in x around 0

       \[\leadsto \color{blue}{x \cdot \left(1 + y \cdot \left(\frac{1}{2} \cdot \left({t}^{2} \cdot y\right) - t\right)\right)} \]
   12. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + y \cdot \left(\frac{1}{2} \cdot \left({t}^{2} \cdot y\right) - t\right)\right)}\right) \]

       2. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(y \cdot \left(\frac{1}{2} \cdot \left({t}^{2} \cdot y\right) - t\right)\right)}\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{1}{2} \cdot \left({t}^{2} \cdot y\right) - t\right)}\right)\right)\right) \]

       4. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\left(\frac{1}{2} \cdot \left({t}^{2} \cdot y\right)\right), \color{blue}{t}\right)\right)\right)\right) \]

       5. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\left(\left(\frac{1}{2} \cdot {t}^{2}\right) \cdot y\right), t\right)\right)\right)\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\left(\frac{1}{2} \cdot {t}^{2}\right), y\right), t\right)\right)\right)\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left({t}^{2}\right)\right), y\right), t\right)\right)\right)\right) \]

       8. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left(t \cdot t\right)\right), y\right), t\right)\right)\right)\right) \]

       9. *-lowering-*.f64 61.9%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(t, t\right)\right), y\right), t\right)\right)\right)\right) \]

   13. Simplified 61.9%

       \[\leadsto \color{blue}{x \cdot \left(1 + y \cdot \left(\left(0.5 \cdot \left(t \cdot t\right)\right) \cdot y - t\right)\right)} \]

   if 0.80000000000000004 < y

   1. Initial program 98.2%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 98.2%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(t \cdot y\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\left(y \cdot t\right)\right)\right) \]

      2. *-lowering-*.f64 58.3%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, t\right)\right)\right) \]

   7. Simplified 58.3%

      \[\leadsto \frac{x}{e^{\color{blue}{y \cdot t}}} \]

   8. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x + y \cdot \left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) - t \cdot x\right)} \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot \left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) - t \cdot x\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) - t \cdot x\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right)\right), \color{blue}{\left(t \cdot x\right)}\right)\right)\right) \]

   10. Simplified 25.3%

       \[\leadsto \color{blue}{x + y \cdot \left(y \cdot \left(0.5 \cdot \left(x \cdot \left(t \cdot t\right)\right)\right) - x \cdot t\right)} \]

   11. Taylor expanded in y around inf

       \[\leadsto \color{blue}{\frac{1}{2} \cdot \left({t}^{2} \cdot \left(x \cdot {y}^{2}\right)\right)} \]
   12. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \left({t}^{2} \cdot \left(x \cdot {y}^{2}\right)\right) \cdot \color{blue}{\frac{1}{2}} \]

       2. *-commutative N/A

          \[\leadsto \left(\left(x \cdot {y}^{2}\right) \cdot {t}^{2}\right) \cdot \frac{1}{2} \]

       3. *-commutative N/A

          \[\leadsto \left(\left({y}^{2} \cdot x\right) \cdot {t}^{2}\right) \cdot \frac{1}{2} \]

       4. associate-*l* N/A

          \[\leadsto \left({y}^{2} \cdot \left(x \cdot {t}^{2}\right)\right) \cdot \frac{1}{2} \]

       5. *-commutative N/A

          \[\leadsto \left({y}^{2} \cdot \left({t}^{2} \cdot x\right)\right) \cdot \frac{1}{2} \]

       6. associate-*r* N/A

          \[\leadsto {y}^{2} \cdot \color{blue}{\left(\left({t}^{2} \cdot x\right) \cdot \frac{1}{2}\right)} \]

       7. *-commutative N/A

          \[\leadsto {y}^{2} \cdot \left(\frac{1}{2} \cdot \color{blue}{\left({t}^{2} \cdot x\right)}\right) \]

       8. unpow2 N/A

          \[\leadsto \left(y \cdot y\right) \cdot \left(\color{blue}{\frac{1}{2}} \cdot \left({t}^{2} \cdot x\right)\right) \]

       9. associate-*l* N/A

          \[\leadsto y \cdot \color{blue}{\left(y \cdot \left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right)} \]

       10. *-commutative N/A

           \[\leadsto y \cdot \left(y \cdot \left(\left({t}^{2} \cdot x\right) \cdot \color{blue}{\frac{1}{2}}\right)\right) \]

       11. associate-*r* N/A

           \[\leadsto y \cdot \left(\left(y \cdot \left({t}^{2} \cdot x\right)\right) \cdot \color{blue}{\frac{1}{2}}\right) \]

       12. *-commutative N/A

           \[\leadsto y \cdot \left(\left(y \cdot \left(x \cdot {t}^{2}\right)\right) \cdot \frac{1}{2}\right) \]

       13. associate-*l* N/A

           \[\leadsto y \cdot \left(\left(\left(y \cdot x\right) \cdot {t}^{2}\right) \cdot \frac{1}{2}\right) \]

       14. *-commutative N/A

           \[\leadsto y \cdot \left(\left(\left(x \cdot y\right) \cdot {t}^{2}\right) \cdot \frac{1}{2}\right) \]

       15. *-commutative N/A

           \[\leadsto y \cdot \left(\left({t}^{2} \cdot \left(x \cdot y\right)\right) \cdot \frac{1}{2}\right) \]

       16. *-commutative N/A

           \[\leadsto y \cdot \left(\frac{1}{2} \cdot \color{blue}{\left({t}^{2} \cdot \left(x \cdot y\right)\right)}\right) \]

       17. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{1}{2} \cdot \left({t}^{2} \cdot \left(x \cdot y\right)\right)\right)}\right) \]

       18. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{\left({t}^{2} \cdot \left(x \cdot y\right)\right)}\right)\right) \]

       19. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(\frac{1}{2}, \left(\left(x \cdot y\right) \cdot \color{blue}{{t}^{2}}\right)\right)\right) \]

       20. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(\frac{1}{2}, \left(\left(y \cdot x\right) \cdot {\color{blue}{t}}^{2}\right)\right)\right) \]

       21. associate-*l* N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(\frac{1}{2}, \left(y \cdot \color{blue}{\left(x \cdot {t}^{2}\right)}\right)\right)\right) \]

   13. Simplified 52.7%

       \[\leadsto \color{blue}{y \cdot \left(0.5 \cdot \left(y \cdot \left(x \cdot \left(t \cdot t\right)\right)\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 59.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+241}:\\ \;\;\;\;\frac{x}{0.5 \cdot \left(a \cdot \left(a \cdot \left(b \cdot b\right)\right)\right)}\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{+69}:\\ \;\;\;\;\frac{x}{t \cdot \left(y + \left(y \cdot y\right) \cdot \left(t \cdot 0.5\right)\right) + 1}\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-55}:\\ \;\;\;\;\frac{2 \cdot \frac{x}{a \cdot a}}{b \cdot b}\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-201}:\\ \;\;\;\;\frac{x}{b \cdot \left(a + b \cdot \left(0.5 \cdot \left(a \cdot a\right)\right)\right) + 1}\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{-141}:\\ \;\;\;\;x + b \cdot \left(b \cdot \left(x \cdot \left(0.5 \cdot \left(a \cdot a\right)\right)\right) - x \cdot a\right)\\ \mathbf{elif}\;y \leq 0.8:\\ \;\;\;\;x \cdot \left(y \cdot \left(y \cdot \left(\left(t \cdot t\right) \cdot 0.5\right) - t\right) + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(0.5 \cdot \left(y \cdot \left(x \cdot \left(t \cdot t\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 46.3% accurate, 7.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+241}:\\ \;\;\;\;\frac{x}{0.5 \cdot \left(a \cdot \left(a \cdot \left(b \cdot b\right)\right)\right)}\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{+71}:\\ \;\;\;\;\frac{x}{t \cdot \left(y + \left(y \cdot y\right) \cdot \left(t \cdot 0.5\right)\right) + 1}\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-55}:\\ \;\;\;\;\frac{2 \cdot \frac{x}{a \cdot a}}{b \cdot b}\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-201}:\\ \;\;\;\;\frac{x}{b \cdot \left(a + b \cdot \left(0.5 \cdot \left(a \cdot a\right)\right)\right) + 1}\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-7}:\\ \;\;\;\;x + b \cdot \left(a \cdot \left(0.5 \cdot \left(a \cdot \left(x \cdot b\right)\right) - x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(0.5 \cdot \left(y \cdot \left(x \cdot \left(t \cdot t\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -8e+241)
   (/ x (* 0.5 (* a (* a (* b b)))))
   (if (<= y -1.7e+71)
     (/ x (+ (* t (+ y (* (* y y) (* t 0.5)))) 1.0))
     (if (<= y -2.3e-55)
       (/ (* 2.0 (/ x (* a a))) (* b b))
       (if (<= y -1.45e-201)
         (/ x (+ (* b (+ a (* b (* 0.5 (* a a))))) 1.0))
         (if (<= y 1.45e-7)
           (+ x (* b (* a (- (* 0.5 (* a (* x b))) x))))
           (* y (* 0.5 (* y (* x (* t t)))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -8e+241) {
		tmp = x / (0.5 * (a * (a * (b * b))));
	} else if (y <= -1.7e+71) {
		tmp = x / ((t * (y + ((y * y) * (t * 0.5)))) + 1.0);
	} else if (y <= -2.3e-55) {
		tmp = (2.0 * (x / (a * a))) / (b * b);
	} else if (y <= -1.45e-201) {
		tmp = x / ((b * (a + (b * (0.5 * (a * a))))) + 1.0);
	} else if (y <= 1.45e-7) {
		tmp = x + (b * (a * ((0.5 * (a * (x * b))) - x)));
	} else {
		tmp = y * (0.5 * (y * (x * (t * t))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-8d+241)) then
        tmp = x / (0.5d0 * (a * (a * (b * b))))
    else if (y <= (-1.7d+71)) then
        tmp = x / ((t * (y + ((y * y) * (t * 0.5d0)))) + 1.0d0)
    else if (y <= (-2.3d-55)) then
        tmp = (2.0d0 * (x / (a * a))) / (b * b)
    else if (y <= (-1.45d-201)) then
        tmp = x / ((b * (a + (b * (0.5d0 * (a * a))))) + 1.0d0)
    else if (y <= 1.45d-7) then
        tmp = x + (b * (a * ((0.5d0 * (a * (x * b))) - x)))
    else
        tmp = y * (0.5d0 * (y * (x * (t * t))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -8e+241) {
		tmp = x / (0.5 * (a * (a * (b * b))));
	} else if (y <= -1.7e+71) {
		tmp = x / ((t * (y + ((y * y) * (t * 0.5)))) + 1.0);
	} else if (y <= -2.3e-55) {
		tmp = (2.0 * (x / (a * a))) / (b * b);
	} else if (y <= -1.45e-201) {
		tmp = x / ((b * (a + (b * (0.5 * (a * a))))) + 1.0);
	} else if (y <= 1.45e-7) {
		tmp = x + (b * (a * ((0.5 * (a * (x * b))) - x)));
	} else {
		tmp = y * (0.5 * (y * (x * (t * t))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -8e+241:
		tmp = x / (0.5 * (a * (a * (b * b))))
	elif y <= -1.7e+71:
		tmp = x / ((t * (y + ((y * y) * (t * 0.5)))) + 1.0)
	elif y <= -2.3e-55:
		tmp = (2.0 * (x / (a * a))) / (b * b)
	elif y <= -1.45e-201:
		tmp = x / ((b * (a + (b * (0.5 * (a * a))))) + 1.0)
	elif y <= 1.45e-7:
		tmp = x + (b * (a * ((0.5 * (a * (x * b))) - x)))
	else:
		tmp = y * (0.5 * (y * (x * (t * t))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -8e+241)
		tmp = Float64(x / Float64(0.5 * Float64(a * Float64(a * Float64(b * b)))));
	elseif (y <= -1.7e+71)
		tmp = Float64(x / Float64(Float64(t * Float64(y + Float64(Float64(y * y) * Float64(t * 0.5)))) + 1.0));
	elseif (y <= -2.3e-55)
		tmp = Float64(Float64(2.0 * Float64(x / Float64(a * a))) / Float64(b * b));
	elseif (y <= -1.45e-201)
		tmp = Float64(x / Float64(Float64(b * Float64(a + Float64(b * Float64(0.5 * Float64(a * a))))) + 1.0));
	elseif (y <= 1.45e-7)
		tmp = Float64(x + Float64(b * Float64(a * Float64(Float64(0.5 * Float64(a * Float64(x * b))) - x))));
	else
		tmp = Float64(y * Float64(0.5 * Float64(y * Float64(x * Float64(t * t)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -8e+241)
		tmp = x / (0.5 * (a * (a * (b * b))));
	elseif (y <= -1.7e+71)
		tmp = x / ((t * (y + ((y * y) * (t * 0.5)))) + 1.0);
	elseif (y <= -2.3e-55)
		tmp = (2.0 * (x / (a * a))) / (b * b);
	elseif (y <= -1.45e-201)
		tmp = x / ((b * (a + (b * (0.5 * (a * a))))) + 1.0);
	elseif (y <= 1.45e-7)
		tmp = x + (b * (a * ((0.5 * (a * (x * b))) - x)));
	else
		tmp = y * (0.5 * (y * (x * (t * t))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -8e+241], N[(x / N[(0.5 * N[(a * N[(a * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.7e+71], N[(x / N[(N[(t * N[(y + N[(N[(y * y), $MachinePrecision] * N[(t * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.3e-55], N[(N[(2.0 * N[(x / N[(a * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(b * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.45e-201], N[(x / N[(N[(b * N[(a + N[(b * N[(0.5 * N[(a * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.45e-7], N[(x + N[(b * N[(a * N[(N[(0.5 * N[(a * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(0.5 * N[(y * N[(x * N[(t * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -8.0000000000000004e241

   1. Initial program 100.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(a \cdot b\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 14.7%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, b\right)\right)\right) \]

   7. Simplified 14.7%

      \[\leadsto \frac{x}{e^{\color{blue}{a \cdot b}}} \]

   8. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + b \cdot \left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)\right)}\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(b \cdot \left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \color{blue}{\left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \color{blue}{\left(\frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right)\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(\left(\frac{1}{2} \cdot {a}^{2}\right) \cdot \color{blue}{b}\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\left(\frac{1}{2} \cdot {a}^{2}\right), \color{blue}{b}\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left({a}^{2}\right)\right), b\right)\right)\right)\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left(a \cdot a\right)\right), b\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 3.5%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(a, a\right)\right), b\right)\right)\right)\right)\right) \]

   10. Simplified 3.5%

       \[\leadsto \frac{x}{\color{blue}{1 + b \cdot \left(a + \left(0.5 \cdot \left(a \cdot a\right)\right) \cdot b\right)}} \]
   11. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(b \cdot \color{blue}{\left(\frac{1}{2} \cdot \left(a \cdot a\right)\right)}\right)\right)\right)\right)\right) \]

       2. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(b \cdot \left(\left(\frac{1}{2} \cdot a\right) \cdot \color{blue}{a}\right)\right)\right)\right)\right)\right) \]

       3. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(\left(b \cdot \left(\frac{1}{2} \cdot a\right)\right) \cdot \color{blue}{a}\right)\right)\right)\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\left(b \cdot \left(\frac{1}{2} \cdot a\right)\right), \color{blue}{a}\right)\right)\right)\right)\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \left(\frac{1}{2} \cdot a\right)\right), a\right)\right)\right)\right)\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \left(a \cdot \frac{1}{2}\right)\right), a\right)\right)\right)\right)\right) \]

       7. *-lowering-*.f64 3.8%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \frac{1}{2}\right)\right), a\right)\right)\right)\right)\right) \]

   12. Applied egg-rr 3.8%

       \[\leadsto \frac{x}{1 + b \cdot \left(a + \color{blue}{\left(b \cdot \left(a \cdot 0.5\right)\right) \cdot a}\right)} \]

   13. Taylor expanded in b around inf

       \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(\frac{1}{2} \cdot \left({a}^{2} \cdot {b}^{2}\right)\right)}\right) \]
   14. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{\left({a}^{2} \cdot {b}^{2}\right)}\right)\right) \]

       2. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{2}, \left(\left(a \cdot a\right) \cdot {\color{blue}{b}}^{2}\right)\right)\right) \]

       3. associate-*l* N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{2}, \left(a \cdot \color{blue}{\left(a \cdot {b}^{2}\right)}\right)\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(a, \color{blue}{\left(a \cdot {b}^{2}\right)}\right)\right)\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(a, \color{blue}{\left({b}^{2}\right)}\right)\right)\right)\right) \]

       6. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(a, \left(b \cdot \color{blue}{b}\right)\right)\right)\right)\right) \]

       7. *-lowering-*.f64 54.4%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(b, \color{blue}{b}\right)\right)\right)\right)\right) \]

   15. Simplified 54.4%

       \[\leadsto \frac{x}{\color{blue}{0.5 \cdot \left(a \cdot \left(a \cdot \left(b \cdot b\right)\right)\right)}} \]

   if -8.0000000000000004e241 < y < -1.6999999999999999e71

   1. Initial program 100.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(t \cdot y\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\left(y \cdot t\right)\right)\right) \]

      2. *-lowering-*.f64 82.7%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, t\right)\right)\right) \]

   7. Simplified 82.7%

      \[\leadsto \frac{x}{e^{\color{blue}{y \cdot t}}} \]

   8. Taylor expanded in t around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + t \cdot \left(y + \frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right)\right)}\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(t \cdot \left(y + \frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \color{blue}{\left(y + \frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right)}\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(y, \color{blue}{\left(\frac{1}{2} \cdot \left(t \cdot {y}^{2}\right)\right)}\right)\right)\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(y, \left(\left(\frac{1}{2} \cdot t\right) \cdot \color{blue}{{y}^{2}}\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(\left(\frac{1}{2} \cdot t\right), \color{blue}{\left({y}^{2}\right)}\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, t\right), \left({\color{blue}{y}}^{2}\right)\right)\right)\right)\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, t\right), \left(y \cdot \color{blue}{y}\right)\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 61.8%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(t, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, t\right), \mathsf{*.f64}\left(y, \color{blue}{y}\right)\right)\right)\right)\right)\right) \]

   10. Simplified 61.8%

       \[\leadsto \frac{x}{\color{blue}{1 + t \cdot \left(y + \left(0.5 \cdot t\right) \cdot \left(y \cdot y\right)\right)}} \]

   if -1.6999999999999999e71 < y < -2.30000000000000011e-55

   1. Initial program 96.6%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 96.6%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(a \cdot b\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 42.4%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, b\right)\right)\right) \]

   7. Simplified 42.4%

      \[\leadsto \frac{x}{e^{\color{blue}{a \cdot b}}} \]

   8. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + b \cdot \left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)\right)}\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(b \cdot \left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \color{blue}{\left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \color{blue}{\left(\frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right)\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(\left(\frac{1}{2} \cdot {a}^{2}\right) \cdot \color{blue}{b}\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\left(\frac{1}{2} \cdot {a}^{2}\right), \color{blue}{b}\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left({a}^{2}\right)\right), b\right)\right)\right)\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left(a \cdot a\right)\right), b\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 22.2%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(a, a\right)\right), b\right)\right)\right)\right)\right) \]

   10. Simplified 22.2%

       \[\leadsto \frac{x}{\color{blue}{1 + b \cdot \left(a + \left(0.5 \cdot \left(a \cdot a\right)\right) \cdot b\right)}} \]
   11. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(b \cdot \color{blue}{\left(\frac{1}{2} \cdot \left(a \cdot a\right)\right)}\right)\right)\right)\right)\right) \]

       2. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(b \cdot \left(\left(\frac{1}{2} \cdot a\right) \cdot \color{blue}{a}\right)\right)\right)\right)\right)\right) \]

       3. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(\left(b \cdot \left(\frac{1}{2} \cdot a\right)\right) \cdot \color{blue}{a}\right)\right)\right)\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\left(b \cdot \left(\frac{1}{2} \cdot a\right)\right), \color{blue}{a}\right)\right)\right)\right)\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \left(\frac{1}{2} \cdot a\right)\right), a\right)\right)\right)\right)\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \left(a \cdot \frac{1}{2}\right)\right), a\right)\right)\right)\right)\right) \]

       7. *-lowering-*.f64 22.2%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \frac{1}{2}\right)\right), a\right)\right)\right)\right)\right) \]

   12. Applied egg-rr 22.2%

       \[\leadsto \frac{x}{1 + b \cdot \left(a + \color{blue}{\left(b \cdot \left(a \cdot 0.5\right)\right) \cdot a}\right)} \]

   13. Taylor expanded in b around inf

       \[\leadsto \color{blue}{2 \cdot \frac{x}{{a}^{2} \cdot {b}^{2}}} \]
   14. Step-by-step derivation

       1. associate-/r* N/A

          \[\leadsto 2 \cdot \frac{\frac{x}{{a}^{2}}}{\color{blue}{{b}^{2}}} \]

       2. associate-*r/ N/A

          \[\leadsto \frac{2 \cdot \frac{x}{{a}^{2}}}{\color{blue}{{b}^{2}}} \]

       3. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left(2 \cdot \frac{x}{{a}^{2}}\right), \color{blue}{\left({b}^{2}\right)}\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(2, \left(\frac{x}{{a}^{2}}\right)\right), \left({\color{blue}{b}}^{2}\right)\right) \]

       5. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(2, \mathsf{/.f64}\left(x, \left({a}^{2}\right)\right)\right), \left({b}^{2}\right)\right) \]

       6. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(2, \mathsf{/.f64}\left(x, \left(a \cdot a\right)\right)\right), \left({b}^{2}\right)\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(2, \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, a\right)\right)\right), \left({b}^{2}\right)\right) \]

       8. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(2, \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, a\right)\right)\right), \left(b \cdot \color{blue}{b}\right)\right) \]

       9. *-lowering-*.f64 52.7%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(2, \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, a\right)\right)\right), \mathsf{*.f64}\left(b, \color{blue}{b}\right)\right) \]

   15. Simplified 52.7%

       \[\leadsto \color{blue}{\frac{2 \cdot \frac{x}{a \cdot a}}{b \cdot b}} \]

   if -2.30000000000000011e-55 < y < -1.4500000000000001e-201

   1. Initial program 91.4%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 91.4%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(a \cdot b\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 71.8%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, b\right)\right)\right) \]

   7. Simplified 71.8%

      \[\leadsto \frac{x}{e^{\color{blue}{a \cdot b}}} \]

   8. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + b \cdot \left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)\right)}\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(b \cdot \left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \color{blue}{\left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \color{blue}{\left(\frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right)\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(\left(\frac{1}{2} \cdot {a}^{2}\right) \cdot \color{blue}{b}\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\left(\frac{1}{2} \cdot {a}^{2}\right), \color{blue}{b}\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left({a}^{2}\right)\right), b\right)\right)\right)\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left(a \cdot a\right)\right), b\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 60.1%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(a, a\right)\right), b\right)\right)\right)\right)\right) \]

   10. Simplified 60.1%

       \[\leadsto \frac{x}{\color{blue}{1 + b \cdot \left(a + \left(0.5 \cdot \left(a \cdot a\right)\right) \cdot b\right)}} \]

   if -1.4500000000000001e-201 < y < 1.4499999999999999e-7

   1. Initial program 94.7%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 94.7%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(a \cdot b\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 81.1%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, b\right)\right)\right) \]

   7. Simplified 81.1%

      \[\leadsto \frac{x}{e^{\color{blue}{a \cdot b}}} \]

   8. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + b \cdot \left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)\right)}\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(b \cdot \left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \color{blue}{\left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \color{blue}{\left(\frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right)\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(\left(\frac{1}{2} \cdot {a}^{2}\right) \cdot \color{blue}{b}\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\left(\frac{1}{2} \cdot {a}^{2}\right), \color{blue}{b}\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left({a}^{2}\right)\right), b\right)\right)\right)\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left(a \cdot a\right)\right), b\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 47.1%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(a, a\right)\right), b\right)\right)\right)\right)\right) \]

   10. Simplified 47.1%

       \[\leadsto \frac{x}{\color{blue}{1 + b \cdot \left(a + \left(0.5 \cdot \left(a \cdot a\right)\right) \cdot b\right)}} \]

   11. Taylor expanded in b around 0

       \[\leadsto \color{blue}{x + b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left({a}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({a}^{2} \cdot x\right)\right)\right) - a \cdot x\right)} \]

   13. Simplified 58.1%

       \[\leadsto \color{blue}{x + b \cdot \left(a \cdot \left(0.5 \cdot \left(a \cdot \left(x \cdot b\right)\right) - x\right)\right)} \]

   if 1.4499999999999999e-7 < y

   1. Initial program 98.2%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 98.2%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(t \cdot y\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\left(y \cdot t\right)\right)\right) \]

      2. *-lowering-*.f64 58.3%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, t\right)\right)\right) \]

   7. Simplified 58.3%

      \[\leadsto \frac{x}{e^{\color{blue}{y \cdot t}}} \]

   8. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x + y \cdot \left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) - t \cdot x\right)} \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot \left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) - t \cdot x\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) - t \cdot x\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right)\right), \color{blue}{\left(t \cdot x\right)}\right)\right)\right) \]

   10. Simplified 25.3%

       \[\leadsto \color{blue}{x + y \cdot \left(y \cdot \left(0.5 \cdot \left(x \cdot \left(t \cdot t\right)\right)\right) - x \cdot t\right)} \]

   11. Taylor expanded in y around inf

       \[\leadsto \color{blue}{\frac{1}{2} \cdot \left({t}^{2} \cdot \left(x \cdot {y}^{2}\right)\right)} \]
   12. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \left({t}^{2} \cdot \left(x \cdot {y}^{2}\right)\right) \cdot \color{blue}{\frac{1}{2}} \]

       2. *-commutative N/A

          \[\leadsto \left(\left(x \cdot {y}^{2}\right) \cdot {t}^{2}\right) \cdot \frac{1}{2} \]

       3. *-commutative N/A

          \[\leadsto \left(\left({y}^{2} \cdot x\right) \cdot {t}^{2}\right) \cdot \frac{1}{2} \]

       4. associate-*l* N/A

          \[\leadsto \left({y}^{2} \cdot \left(x \cdot {t}^{2}\right)\right) \cdot \frac{1}{2} \]

       5. *-commutative N/A

          \[\leadsto \left({y}^{2} \cdot \left({t}^{2} \cdot x\right)\right) \cdot \frac{1}{2} \]

       6. associate-*r* N/A

          \[\leadsto {y}^{2} \cdot \color{blue}{\left(\left({t}^{2} \cdot x\right) \cdot \frac{1}{2}\right)} \]

       7. *-commutative N/A

          \[\leadsto {y}^{2} \cdot \left(\frac{1}{2} \cdot \color{blue}{\left({t}^{2} \cdot x\right)}\right) \]

       8. unpow2 N/A

          \[\leadsto \left(y \cdot y\right) \cdot \left(\color{blue}{\frac{1}{2}} \cdot \left({t}^{2} \cdot x\right)\right) \]

       9. associate-*l* N/A

          \[\leadsto y \cdot \color{blue}{\left(y \cdot \left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right)} \]

       10. *-commutative N/A

           \[\leadsto y \cdot \left(y \cdot \left(\left({t}^{2} \cdot x\right) \cdot \color{blue}{\frac{1}{2}}\right)\right) \]

       11. associate-*r* N/A

           \[\leadsto y \cdot \left(\left(y \cdot \left({t}^{2} \cdot x\right)\right) \cdot \color{blue}{\frac{1}{2}}\right) \]

       12. *-commutative N/A

           \[\leadsto y \cdot \left(\left(y \cdot \left(x \cdot {t}^{2}\right)\right) \cdot \frac{1}{2}\right) \]

       13. associate-*l* N/A

           \[\leadsto y \cdot \left(\left(\left(y \cdot x\right) \cdot {t}^{2}\right) \cdot \frac{1}{2}\right) \]

       14. *-commutative N/A

           \[\leadsto y \cdot \left(\left(\left(x \cdot y\right) \cdot {t}^{2}\right) \cdot \frac{1}{2}\right) \]

       15. *-commutative N/A

           \[\leadsto y \cdot \left(\left({t}^{2} \cdot \left(x \cdot y\right)\right) \cdot \frac{1}{2}\right) \]

       16. *-commutative N/A

           \[\leadsto y \cdot \left(\frac{1}{2} \cdot \color{blue}{\left({t}^{2} \cdot \left(x \cdot y\right)\right)}\right) \]

       17. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{1}{2} \cdot \left({t}^{2} \cdot \left(x \cdot y\right)\right)\right)}\right) \]

       18. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{\left({t}^{2} \cdot \left(x \cdot y\right)\right)}\right)\right) \]

       19. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(\frac{1}{2}, \left(\left(x \cdot y\right) \cdot \color{blue}{{t}^{2}}\right)\right)\right) \]

       20. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(\frac{1}{2}, \left(\left(y \cdot x\right) \cdot {\color{blue}{t}}^{2}\right)\right)\right) \]

       21. associate-*l* N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(\frac{1}{2}, \left(y \cdot \color{blue}{\left(x \cdot {t}^{2}\right)}\right)\right)\right) \]

   13. Simplified 52.7%

       \[\leadsto \color{blue}{y \cdot \left(0.5 \cdot \left(y \cdot \left(x \cdot \left(t \cdot t\right)\right)\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 56.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+241}:\\ \;\;\;\;\frac{x}{0.5 \cdot \left(a \cdot \left(a \cdot \left(b \cdot b\right)\right)\right)}\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{+71}:\\ \;\;\;\;\frac{x}{t \cdot \left(y + \left(y \cdot y\right) \cdot \left(t \cdot 0.5\right)\right) + 1}\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-55}:\\ \;\;\;\;\frac{2 \cdot \frac{x}{a \cdot a}}{b \cdot b}\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-201}:\\ \;\;\;\;\frac{x}{b \cdot \left(a + b \cdot \left(0.5 \cdot \left(a \cdot a\right)\right)\right) + 1}\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-7}:\\ \;\;\;\;x + b \cdot \left(a \cdot \left(0.5 \cdot \left(a \cdot \left(x \cdot b\right)\right) - x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(0.5 \cdot \left(y \cdot \left(x \cdot \left(t \cdot t\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 45.7% accurate, 7.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+241}:\\ \;\;\;\;\frac{x}{0.5 \cdot \left(a \cdot \left(a \cdot \left(b \cdot b\right)\right)\right)}\\ \mathbf{elif}\;y \leq -3 \cdot 10^{+102}:\\ \;\;\;\;\frac{x}{y \cdot t + 1}\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-55}:\\ \;\;\;\;\frac{2 \cdot \frac{x}{a \cdot a}}{b \cdot b}\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-200}:\\ \;\;\;\;\frac{x}{b \cdot \left(a + b \cdot \left(0.5 \cdot \left(a \cdot a\right)\right)\right) + 1}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-5}:\\ \;\;\;\;x + b \cdot \left(a \cdot \left(0.5 \cdot \left(a \cdot \left(x \cdot b\right)\right) - x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(0.5 \cdot \left(y \cdot \left(x \cdot \left(t \cdot t\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -8e+241)
   (/ x (* 0.5 (* a (* a (* b b)))))
   (if (<= y -3e+102)
     (/ x (+ (* y t) 1.0))
     (if (<= y -2.1e-55)
       (/ (* 2.0 (/ x (* a a))) (* b b))
       (if (<= y -1.3e-200)
         (/ x (+ (* b (+ a (* b (* 0.5 (* a a))))) 1.0))
         (if (<= y 2.4e-5)
           (+ x (* b (* a (- (* 0.5 (* a (* x b))) x))))
           (* y (* 0.5 (* y (* x (* t t)))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -8e+241) {
		tmp = x / (0.5 * (a * (a * (b * b))));
	} else if (y <= -3e+102) {
		tmp = x / ((y * t) + 1.0);
	} else if (y <= -2.1e-55) {
		tmp = (2.0 * (x / (a * a))) / (b * b);
	} else if (y <= -1.3e-200) {
		tmp = x / ((b * (a + (b * (0.5 * (a * a))))) + 1.0);
	} else if (y <= 2.4e-5) {
		tmp = x + (b * (a * ((0.5 * (a * (x * b))) - x)));
	} else {
		tmp = y * (0.5 * (y * (x * (t * t))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-8d+241)) then
        tmp = x / (0.5d0 * (a * (a * (b * b))))
    else if (y <= (-3d+102)) then
        tmp = x / ((y * t) + 1.0d0)
    else if (y <= (-2.1d-55)) then
        tmp = (2.0d0 * (x / (a * a))) / (b * b)
    else if (y <= (-1.3d-200)) then
        tmp = x / ((b * (a + (b * (0.5d0 * (a * a))))) + 1.0d0)
    else if (y <= 2.4d-5) then
        tmp = x + (b * (a * ((0.5d0 * (a * (x * b))) - x)))
    else
        tmp = y * (0.5d0 * (y * (x * (t * t))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -8e+241) {
		tmp = x / (0.5 * (a * (a * (b * b))));
	} else if (y <= -3e+102) {
		tmp = x / ((y * t) + 1.0);
	} else if (y <= -2.1e-55) {
		tmp = (2.0 * (x / (a * a))) / (b * b);
	} else if (y <= -1.3e-200) {
		tmp = x / ((b * (a + (b * (0.5 * (a * a))))) + 1.0);
	} else if (y <= 2.4e-5) {
		tmp = x + (b * (a * ((0.5 * (a * (x * b))) - x)));
	} else {
		tmp = y * (0.5 * (y * (x * (t * t))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -8e+241:
		tmp = x / (0.5 * (a * (a * (b * b))))
	elif y <= -3e+102:
		tmp = x / ((y * t) + 1.0)
	elif y <= -2.1e-55:
		tmp = (2.0 * (x / (a * a))) / (b * b)
	elif y <= -1.3e-200:
		tmp = x / ((b * (a + (b * (0.5 * (a * a))))) + 1.0)
	elif y <= 2.4e-5:
		tmp = x + (b * (a * ((0.5 * (a * (x * b))) - x)))
	else:
		tmp = y * (0.5 * (y * (x * (t * t))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -8e+241)
		tmp = Float64(x / Float64(0.5 * Float64(a * Float64(a * Float64(b * b)))));
	elseif (y <= -3e+102)
		tmp = Float64(x / Float64(Float64(y * t) + 1.0));
	elseif (y <= -2.1e-55)
		tmp = Float64(Float64(2.0 * Float64(x / Float64(a * a))) / Float64(b * b));
	elseif (y <= -1.3e-200)
		tmp = Float64(x / Float64(Float64(b * Float64(a + Float64(b * Float64(0.5 * Float64(a * a))))) + 1.0));
	elseif (y <= 2.4e-5)
		tmp = Float64(x + Float64(b * Float64(a * Float64(Float64(0.5 * Float64(a * Float64(x * b))) - x))));
	else
		tmp = Float64(y * Float64(0.5 * Float64(y * Float64(x * Float64(t * t)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -8e+241)
		tmp = x / (0.5 * (a * (a * (b * b))));
	elseif (y <= -3e+102)
		tmp = x / ((y * t) + 1.0);
	elseif (y <= -2.1e-55)
		tmp = (2.0 * (x / (a * a))) / (b * b);
	elseif (y <= -1.3e-200)
		tmp = x / ((b * (a + (b * (0.5 * (a * a))))) + 1.0);
	elseif (y <= 2.4e-5)
		tmp = x + (b * (a * ((0.5 * (a * (x * b))) - x)));
	else
		tmp = y * (0.5 * (y * (x * (t * t))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -8e+241], N[(x / N[(0.5 * N[(a * N[(a * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3e+102], N[(x / N[(N[(y * t), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.1e-55], N[(N[(2.0 * N[(x / N[(a * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(b * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.3e-200], N[(x / N[(N[(b * N[(a + N[(b * N[(0.5 * N[(a * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.4e-5], N[(x + N[(b * N[(a * N[(N[(0.5 * N[(a * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(0.5 * N[(y * N[(x * N[(t * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -8.0000000000000004e241

   1. Initial program 100.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(a \cdot b\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 14.7%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, b\right)\right)\right) \]

   7. Simplified 14.7%

      \[\leadsto \frac{x}{e^{\color{blue}{a \cdot b}}} \]

   8. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + b \cdot \left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)\right)}\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(b \cdot \left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \color{blue}{\left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \color{blue}{\left(\frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right)\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(\left(\frac{1}{2} \cdot {a}^{2}\right) \cdot \color{blue}{b}\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\left(\frac{1}{2} \cdot {a}^{2}\right), \color{blue}{b}\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left({a}^{2}\right)\right), b\right)\right)\right)\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left(a \cdot a\right)\right), b\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 3.5%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(a, a\right)\right), b\right)\right)\right)\right)\right) \]

   10. Simplified 3.5%

       \[\leadsto \frac{x}{\color{blue}{1 + b \cdot \left(a + \left(0.5 \cdot \left(a \cdot a\right)\right) \cdot b\right)}} \]
   11. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(b \cdot \color{blue}{\left(\frac{1}{2} \cdot \left(a \cdot a\right)\right)}\right)\right)\right)\right)\right) \]

       2. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(b \cdot \left(\left(\frac{1}{2} \cdot a\right) \cdot \color{blue}{a}\right)\right)\right)\right)\right)\right) \]

       3. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(\left(b \cdot \left(\frac{1}{2} \cdot a\right)\right) \cdot \color{blue}{a}\right)\right)\right)\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\left(b \cdot \left(\frac{1}{2} \cdot a\right)\right), \color{blue}{a}\right)\right)\right)\right)\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \left(\frac{1}{2} \cdot a\right)\right), a\right)\right)\right)\right)\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \left(a \cdot \frac{1}{2}\right)\right), a\right)\right)\right)\right)\right) \]

       7. *-lowering-*.f64 3.8%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \frac{1}{2}\right)\right), a\right)\right)\right)\right)\right) \]

   12. Applied egg-rr 3.8%

       \[\leadsto \frac{x}{1 + b \cdot \left(a + \color{blue}{\left(b \cdot \left(a \cdot 0.5\right)\right) \cdot a}\right)} \]

   13. Taylor expanded in b around inf

       \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(\frac{1}{2} \cdot \left({a}^{2} \cdot {b}^{2}\right)\right)}\right) \]
   14. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{\left({a}^{2} \cdot {b}^{2}\right)}\right)\right) \]

       2. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{2}, \left(\left(a \cdot a\right) \cdot {\color{blue}{b}}^{2}\right)\right)\right) \]

       3. associate-*l* N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{2}, \left(a \cdot \color{blue}{\left(a \cdot {b}^{2}\right)}\right)\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(a, \color{blue}{\left(a \cdot {b}^{2}\right)}\right)\right)\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(a, \color{blue}{\left({b}^{2}\right)}\right)\right)\right)\right) \]

       6. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(a, \left(b \cdot \color{blue}{b}\right)\right)\right)\right)\right) \]

       7. *-lowering-*.f64 54.4%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(b, \color{blue}{b}\right)\right)\right)\right)\right) \]

   15. Simplified 54.4%

       \[\leadsto \frac{x}{\color{blue}{0.5 \cdot \left(a \cdot \left(a \cdot \left(b \cdot b\right)\right)\right)}} \]

   if -8.0000000000000004e241 < y < -2.9999999999999998e102

   1. Initial program 100.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(t \cdot y\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\left(y \cdot t\right)\right)\right) \]

      2. *-lowering-*.f64 90.8%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, t\right)\right)\right) \]

   7. Simplified 90.8%

      \[\leadsto \frac{x}{e^{\color{blue}{y \cdot t}}} \]

   8. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + t \cdot y\right)}\right) \]
   9. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(t \cdot y + \color{blue}{1}\right)\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\left(t \cdot y\right), \color{blue}{1}\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\left(y \cdot t\right), 1\right)\right) \]

      4. *-lowering-*.f64 53.7%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, t\right), 1\right)\right) \]

   10. Simplified 53.7%

       \[\leadsto \frac{x}{\color{blue}{y \cdot t + 1}} \]

   if -2.9999999999999998e102 < y < -2.1000000000000002e-55

   1. Initial program 97.2%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 97.2%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(a \cdot b\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 48.2%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, b\right)\right)\right) \]

   7. Simplified 48.2%

      \[\leadsto \frac{x}{e^{\color{blue}{a \cdot b}}} \]

   8. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + b \cdot \left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)\right)}\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(b \cdot \left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \color{blue}{\left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \color{blue}{\left(\frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right)\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(\left(\frac{1}{2} \cdot {a}^{2}\right) \cdot \color{blue}{b}\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\left(\frac{1}{2} \cdot {a}^{2}\right), \color{blue}{b}\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left({a}^{2}\right)\right), b\right)\right)\right)\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left(a \cdot a\right)\right), b\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 26.5%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(a, a\right)\right), b\right)\right)\right)\right)\right) \]

   10. Simplified 26.5%

       \[\leadsto \frac{x}{\color{blue}{1 + b \cdot \left(a + \left(0.5 \cdot \left(a \cdot a\right)\right) \cdot b\right)}} \]
   11. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(b \cdot \color{blue}{\left(\frac{1}{2} \cdot \left(a \cdot a\right)\right)}\right)\right)\right)\right)\right) \]

       2. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(b \cdot \left(\left(\frac{1}{2} \cdot a\right) \cdot \color{blue}{a}\right)\right)\right)\right)\right)\right) \]

       3. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(\left(b \cdot \left(\frac{1}{2} \cdot a\right)\right) \cdot \color{blue}{a}\right)\right)\right)\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\left(b \cdot \left(\frac{1}{2} \cdot a\right)\right), \color{blue}{a}\right)\right)\right)\right)\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \left(\frac{1}{2} \cdot a\right)\right), a\right)\right)\right)\right)\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \left(a \cdot \frac{1}{2}\right)\right), a\right)\right)\right)\right)\right) \]

       7. *-lowering-*.f64 21.0%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \frac{1}{2}\right)\right), a\right)\right)\right)\right)\right) \]

   12. Applied egg-rr 21.0%

       \[\leadsto \frac{x}{1 + b \cdot \left(a + \color{blue}{\left(b \cdot \left(a \cdot 0.5\right)\right) \cdot a}\right)} \]

   13. Taylor expanded in b around inf

       \[\leadsto \color{blue}{2 \cdot \frac{x}{{a}^{2} \cdot {b}^{2}}} \]
   14. Step-by-step derivation

       1. associate-/r* N/A

          \[\leadsto 2 \cdot \frac{\frac{x}{{a}^{2}}}{\color{blue}{{b}^{2}}} \]

       2. associate-*r/ N/A

          \[\leadsto \frac{2 \cdot \frac{x}{{a}^{2}}}{\color{blue}{{b}^{2}}} \]

       3. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left(2 \cdot \frac{x}{{a}^{2}}\right), \color{blue}{\left({b}^{2}\right)}\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(2, \left(\frac{x}{{a}^{2}}\right)\right), \left({\color{blue}{b}}^{2}\right)\right) \]

       5. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(2, \mathsf{/.f64}\left(x, \left({a}^{2}\right)\right)\right), \left({b}^{2}\right)\right) \]

       6. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(2, \mathsf{/.f64}\left(x, \left(a \cdot a\right)\right)\right), \left({b}^{2}\right)\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(2, \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, a\right)\right)\right), \left({b}^{2}\right)\right) \]

       8. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(2, \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, a\right)\right)\right), \left(b \cdot \color{blue}{b}\right)\right) \]

       9. *-lowering-*.f64 51.0%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(2, \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, a\right)\right)\right), \mathsf{*.f64}\left(b, \color{blue}{b}\right)\right) \]

   15. Simplified 51.0%

       \[\leadsto \color{blue}{\frac{2 \cdot \frac{x}{a \cdot a}}{b \cdot b}} \]

   if -2.1000000000000002e-55 < y < -1.29999999999999995e-200

   1. Initial program 91.4%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 91.4%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(a \cdot b\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 71.8%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, b\right)\right)\right) \]

   7. Simplified 71.8%

      \[\leadsto \frac{x}{e^{\color{blue}{a \cdot b}}} \]

   8. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + b \cdot \left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)\right)}\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(b \cdot \left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \color{blue}{\left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \color{blue}{\left(\frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right)\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(\left(\frac{1}{2} \cdot {a}^{2}\right) \cdot \color{blue}{b}\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\left(\frac{1}{2} \cdot {a}^{2}\right), \color{blue}{b}\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left({a}^{2}\right)\right), b\right)\right)\right)\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left(a \cdot a\right)\right), b\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 60.1%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(a, a\right)\right), b\right)\right)\right)\right)\right) \]

   10. Simplified 60.1%

       \[\leadsto \frac{x}{\color{blue}{1 + b \cdot \left(a + \left(0.5 \cdot \left(a \cdot a\right)\right) \cdot b\right)}} \]

   if -1.29999999999999995e-200 < y < 2.4000000000000001e-5

   1. Initial program 94.7%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 94.7%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(a \cdot b\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 81.1%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, b\right)\right)\right) \]

   7. Simplified 81.1%

      \[\leadsto \frac{x}{e^{\color{blue}{a \cdot b}}} \]

   8. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + b \cdot \left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)\right)}\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(b \cdot \left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \color{blue}{\left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \color{blue}{\left(\frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right)\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(\left(\frac{1}{2} \cdot {a}^{2}\right) \cdot \color{blue}{b}\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\left(\frac{1}{2} \cdot {a}^{2}\right), \color{blue}{b}\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left({a}^{2}\right)\right), b\right)\right)\right)\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left(a \cdot a\right)\right), b\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 47.1%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(a, a\right)\right), b\right)\right)\right)\right)\right) \]

   10. Simplified 47.1%

       \[\leadsto \frac{x}{\color{blue}{1 + b \cdot \left(a + \left(0.5 \cdot \left(a \cdot a\right)\right) \cdot b\right)}} \]

   11. Taylor expanded in b around 0

       \[\leadsto \color{blue}{x + b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left({a}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({a}^{2} \cdot x\right)\right)\right) - a \cdot x\right)} \]

   13. Simplified 58.1%

       \[\leadsto \color{blue}{x + b \cdot \left(a \cdot \left(0.5 \cdot \left(a \cdot \left(x \cdot b\right)\right) - x\right)\right)} \]

   if 2.4000000000000001e-5 < y

   1. Initial program 98.2%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 98.2%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(t \cdot y\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\left(y \cdot t\right)\right)\right) \]

      2. *-lowering-*.f64 58.3%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, t\right)\right)\right) \]

   7. Simplified 58.3%

      \[\leadsto \frac{x}{e^{\color{blue}{y \cdot t}}} \]

   8. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x + y \cdot \left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) - t \cdot x\right)} \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot \left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) - t \cdot x\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) - t \cdot x\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right)\right), \color{blue}{\left(t \cdot x\right)}\right)\right)\right) \]

   10. Simplified 25.3%

       \[\leadsto \color{blue}{x + y \cdot \left(y \cdot \left(0.5 \cdot \left(x \cdot \left(t \cdot t\right)\right)\right) - x \cdot t\right)} \]

   11. Taylor expanded in y around inf

       \[\leadsto \color{blue}{\frac{1}{2} \cdot \left({t}^{2} \cdot \left(x \cdot {y}^{2}\right)\right)} \]
   12. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \left({t}^{2} \cdot \left(x \cdot {y}^{2}\right)\right) \cdot \color{blue}{\frac{1}{2}} \]

       2. *-commutative N/A

          \[\leadsto \left(\left(x \cdot {y}^{2}\right) \cdot {t}^{2}\right) \cdot \frac{1}{2} \]

       3. *-commutative N/A

          \[\leadsto \left(\left({y}^{2} \cdot x\right) \cdot {t}^{2}\right) \cdot \frac{1}{2} \]

       4. associate-*l* N/A

          \[\leadsto \left({y}^{2} \cdot \left(x \cdot {t}^{2}\right)\right) \cdot \frac{1}{2} \]

       5. *-commutative N/A

          \[\leadsto \left({y}^{2} \cdot \left({t}^{2} \cdot x\right)\right) \cdot \frac{1}{2} \]

       6. associate-*r* N/A

          \[\leadsto {y}^{2} \cdot \color{blue}{\left(\left({t}^{2} \cdot x\right) \cdot \frac{1}{2}\right)} \]

       7. *-commutative N/A

          \[\leadsto {y}^{2} \cdot \left(\frac{1}{2} \cdot \color{blue}{\left({t}^{2} \cdot x\right)}\right) \]

       8. unpow2 N/A

          \[\leadsto \left(y \cdot y\right) \cdot \left(\color{blue}{\frac{1}{2}} \cdot \left({t}^{2} \cdot x\right)\right) \]

       9. associate-*l* N/A

          \[\leadsto y \cdot \color{blue}{\left(y \cdot \left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right)} \]

       10. *-commutative N/A

           \[\leadsto y \cdot \left(y \cdot \left(\left({t}^{2} \cdot x\right) \cdot \color{blue}{\frac{1}{2}}\right)\right) \]

       11. associate-*r* N/A

           \[\leadsto y \cdot \left(\left(y \cdot \left({t}^{2} \cdot x\right)\right) \cdot \color{blue}{\frac{1}{2}}\right) \]

       12. *-commutative N/A

           \[\leadsto y \cdot \left(\left(y \cdot \left(x \cdot {t}^{2}\right)\right) \cdot \frac{1}{2}\right) \]

       13. associate-*l* N/A

           \[\leadsto y \cdot \left(\left(\left(y \cdot x\right) \cdot {t}^{2}\right) \cdot \frac{1}{2}\right) \]

       14. *-commutative N/A

           \[\leadsto y \cdot \left(\left(\left(x \cdot y\right) \cdot {t}^{2}\right) \cdot \frac{1}{2}\right) \]

       15. *-commutative N/A

           \[\leadsto y \cdot \left(\left({t}^{2} \cdot \left(x \cdot y\right)\right) \cdot \frac{1}{2}\right) \]

       16. *-commutative N/A

           \[\leadsto y \cdot \left(\frac{1}{2} \cdot \color{blue}{\left({t}^{2} \cdot \left(x \cdot y\right)\right)}\right) \]

       17. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{1}{2} \cdot \left({t}^{2} \cdot \left(x \cdot y\right)\right)\right)}\right) \]

       18. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{\left({t}^{2} \cdot \left(x \cdot y\right)\right)}\right)\right) \]

       19. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(\frac{1}{2}, \left(\left(x \cdot y\right) \cdot \color{blue}{{t}^{2}}\right)\right)\right) \]

       20. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(\frac{1}{2}, \left(\left(y \cdot x\right) \cdot {\color{blue}{t}}^{2}\right)\right)\right) \]

       21. associate-*l* N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(\frac{1}{2}, \left(y \cdot \color{blue}{\left(x \cdot {t}^{2}\right)}\right)\right)\right) \]

   13. Simplified 52.7%

       \[\leadsto \color{blue}{y \cdot \left(0.5 \cdot \left(y \cdot \left(x \cdot \left(t \cdot t\right)\right)\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 55.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+241}:\\ \;\;\;\;\frac{x}{0.5 \cdot \left(a \cdot \left(a \cdot \left(b \cdot b\right)\right)\right)}\\ \mathbf{elif}\;y \leq -3 \cdot 10^{+102}:\\ \;\;\;\;\frac{x}{y \cdot t + 1}\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-55}:\\ \;\;\;\;\frac{2 \cdot \frac{x}{a \cdot a}}{b \cdot b}\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-200}:\\ \;\;\;\;\frac{x}{b \cdot \left(a + b \cdot \left(0.5 \cdot \left(a \cdot a\right)\right)\right) + 1}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-5}:\\ \;\;\;\;x + b \cdot \left(a \cdot \left(0.5 \cdot \left(a \cdot \left(x \cdot b\right)\right) - x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(0.5 \cdot \left(y \cdot \left(x \cdot \left(t \cdot t\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 43.3% accurate, 7.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+241}:\\ \;\;\;\;\frac{x}{0.5 \cdot \left(a \cdot \left(a \cdot \left(b \cdot b\right)\right)\right)}\\ \mathbf{elif}\;y \leq -3 \cdot 10^{+102}:\\ \;\;\;\;\frac{x}{y \cdot t + 1}\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{-59}:\\ \;\;\;\;\frac{2 \cdot \frac{x}{a \cdot a}}{b \cdot b}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-143}:\\ \;\;\;\;x - b \cdot \left(x \cdot a\right)\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-7}:\\ \;\;\;\;x \cdot \left(y \cdot \left(y \cdot \left(\left(t \cdot t\right) \cdot 0.5\right) - t\right) + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(0.5 \cdot \left(y \cdot \left(x \cdot \left(t \cdot t\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -9.5e+241)
   (/ x (* 0.5 (* a (* a (* b b)))))
   (if (<= y -3e+102)
     (/ x (+ (* y t) 1.0))
     (if (<= y -1.25e-59)
       (/ (* 2.0 (/ x (* a a))) (* b b))
       (if (<= y 2.5e-143)
         (- x (* b (* x a)))
         (if (<= y 4e-7)
           (* x (+ (* y (- (* y (* (* t t) 0.5)) t)) 1.0))
           (* y (* 0.5 (* y (* x (* t t)))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -9.5e+241) {
		tmp = x / (0.5 * (a * (a * (b * b))));
	} else if (y <= -3e+102) {
		tmp = x / ((y * t) + 1.0);
	} else if (y <= -1.25e-59) {
		tmp = (2.0 * (x / (a * a))) / (b * b);
	} else if (y <= 2.5e-143) {
		tmp = x - (b * (x * a));
	} else if (y <= 4e-7) {
		tmp = x * ((y * ((y * ((t * t) * 0.5)) - t)) + 1.0);
	} else {
		tmp = y * (0.5 * (y * (x * (t * t))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-9.5d+241)) then
        tmp = x / (0.5d0 * (a * (a * (b * b))))
    else if (y <= (-3d+102)) then
        tmp = x / ((y * t) + 1.0d0)
    else if (y <= (-1.25d-59)) then
        tmp = (2.0d0 * (x / (a * a))) / (b * b)
    else if (y <= 2.5d-143) then
        tmp = x - (b * (x * a))
    else if (y <= 4d-7) then
        tmp = x * ((y * ((y * ((t * t) * 0.5d0)) - t)) + 1.0d0)
    else
        tmp = y * (0.5d0 * (y * (x * (t * t))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -9.5e+241) {
		tmp = x / (0.5 * (a * (a * (b * b))));
	} else if (y <= -3e+102) {
		tmp = x / ((y * t) + 1.0);
	} else if (y <= -1.25e-59) {
		tmp = (2.0 * (x / (a * a))) / (b * b);
	} else if (y <= 2.5e-143) {
		tmp = x - (b * (x * a));
	} else if (y <= 4e-7) {
		tmp = x * ((y * ((y * ((t * t) * 0.5)) - t)) + 1.0);
	} else {
		tmp = y * (0.5 * (y * (x * (t * t))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -9.5e+241:
		tmp = x / (0.5 * (a * (a * (b * b))))
	elif y <= -3e+102:
		tmp = x / ((y * t) + 1.0)
	elif y <= -1.25e-59:
		tmp = (2.0 * (x / (a * a))) / (b * b)
	elif y <= 2.5e-143:
		tmp = x - (b * (x * a))
	elif y <= 4e-7:
		tmp = x * ((y * ((y * ((t * t) * 0.5)) - t)) + 1.0)
	else:
		tmp = y * (0.5 * (y * (x * (t * t))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -9.5e+241)
		tmp = Float64(x / Float64(0.5 * Float64(a * Float64(a * Float64(b * b)))));
	elseif (y <= -3e+102)
		tmp = Float64(x / Float64(Float64(y * t) + 1.0));
	elseif (y <= -1.25e-59)
		tmp = Float64(Float64(2.0 * Float64(x / Float64(a * a))) / Float64(b * b));
	elseif (y <= 2.5e-143)
		tmp = Float64(x - Float64(b * Float64(x * a)));
	elseif (y <= 4e-7)
		tmp = Float64(x * Float64(Float64(y * Float64(Float64(y * Float64(Float64(t * t) * 0.5)) - t)) + 1.0));
	else
		tmp = Float64(y * Float64(0.5 * Float64(y * Float64(x * Float64(t * t)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -9.5e+241)
		tmp = x / (0.5 * (a * (a * (b * b))));
	elseif (y <= -3e+102)
		tmp = x / ((y * t) + 1.0);
	elseif (y <= -1.25e-59)
		tmp = (2.0 * (x / (a * a))) / (b * b);
	elseif (y <= 2.5e-143)
		tmp = x - (b * (x * a));
	elseif (y <= 4e-7)
		tmp = x * ((y * ((y * ((t * t) * 0.5)) - t)) + 1.0);
	else
		tmp = y * (0.5 * (y * (x * (t * t))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -9.5e+241], N[(x / N[(0.5 * N[(a * N[(a * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3e+102], N[(x / N[(N[(y * t), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.25e-59], N[(N[(2.0 * N[(x / N[(a * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(b * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.5e-143], N[(x - N[(b * N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4e-7], N[(x * N[(N[(y * N[(N[(y * N[(N[(t * t), $MachinePrecision] * 0.5), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(y * N[(0.5 * N[(y * N[(x * N[(t * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -9.50000000000000019e241

   1. Initial program 100.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(a \cdot b\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 14.7%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, b\right)\right)\right) \]

   7. Simplified 14.7%

      \[\leadsto \frac{x}{e^{\color{blue}{a \cdot b}}} \]

   8. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + b \cdot \left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)\right)}\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(b \cdot \left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \color{blue}{\left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \color{blue}{\left(\frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right)\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(\left(\frac{1}{2} \cdot {a}^{2}\right) \cdot \color{blue}{b}\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\left(\frac{1}{2} \cdot {a}^{2}\right), \color{blue}{b}\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left({a}^{2}\right)\right), b\right)\right)\right)\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left(a \cdot a\right)\right), b\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 3.5%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(a, a\right)\right), b\right)\right)\right)\right)\right) \]

   10. Simplified 3.5%

       \[\leadsto \frac{x}{\color{blue}{1 + b \cdot \left(a + \left(0.5 \cdot \left(a \cdot a\right)\right) \cdot b\right)}} \]
   11. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(b \cdot \color{blue}{\left(\frac{1}{2} \cdot \left(a \cdot a\right)\right)}\right)\right)\right)\right)\right) \]

       2. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(b \cdot \left(\left(\frac{1}{2} \cdot a\right) \cdot \color{blue}{a}\right)\right)\right)\right)\right)\right) \]

       3. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(\left(b \cdot \left(\frac{1}{2} \cdot a\right)\right) \cdot \color{blue}{a}\right)\right)\right)\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\left(b \cdot \left(\frac{1}{2} \cdot a\right)\right), \color{blue}{a}\right)\right)\right)\right)\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \left(\frac{1}{2} \cdot a\right)\right), a\right)\right)\right)\right)\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \left(a \cdot \frac{1}{2}\right)\right), a\right)\right)\right)\right)\right) \]

       7. *-lowering-*.f64 3.8%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \frac{1}{2}\right)\right), a\right)\right)\right)\right)\right) \]

   12. Applied egg-rr 3.8%

       \[\leadsto \frac{x}{1 + b \cdot \left(a + \color{blue}{\left(b \cdot \left(a \cdot 0.5\right)\right) \cdot a}\right)} \]

   13. Taylor expanded in b around inf

       \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(\frac{1}{2} \cdot \left({a}^{2} \cdot {b}^{2}\right)\right)}\right) \]
   14. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{\left({a}^{2} \cdot {b}^{2}\right)}\right)\right) \]

       2. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{2}, \left(\left(a \cdot a\right) \cdot {\color{blue}{b}}^{2}\right)\right)\right) \]

       3. associate-*l* N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{2}, \left(a \cdot \color{blue}{\left(a \cdot {b}^{2}\right)}\right)\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(a, \color{blue}{\left(a \cdot {b}^{2}\right)}\right)\right)\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(a, \color{blue}{\left({b}^{2}\right)}\right)\right)\right)\right) \]

       6. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(a, \left(b \cdot \color{blue}{b}\right)\right)\right)\right)\right) \]

       7. *-lowering-*.f64 54.4%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(b, \color{blue}{b}\right)\right)\right)\right)\right) \]

   15. Simplified 54.4%

       \[\leadsto \frac{x}{\color{blue}{0.5 \cdot \left(a \cdot \left(a \cdot \left(b \cdot b\right)\right)\right)}} \]

   if -9.50000000000000019e241 < y < -2.9999999999999998e102

   1. Initial program 100.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(t \cdot y\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\left(y \cdot t\right)\right)\right) \]

      2. *-lowering-*.f64 90.8%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, t\right)\right)\right) \]

   7. Simplified 90.8%

      \[\leadsto \frac{x}{e^{\color{blue}{y \cdot t}}} \]

   8. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + t \cdot y\right)}\right) \]
   9. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(t \cdot y + \color{blue}{1}\right)\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\left(t \cdot y\right), \color{blue}{1}\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\left(y \cdot t\right), 1\right)\right) \]

      4. *-lowering-*.f64 53.7%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, t\right), 1\right)\right) \]

   10. Simplified 53.7%

       \[\leadsto \frac{x}{\color{blue}{y \cdot t + 1}} \]

   if -2.9999999999999998e102 < y < -1.25e-59

   1. Initial program 97.3%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 97.3%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(a \cdot b\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 49.6%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, b\right)\right)\right) \]

   7. Simplified 49.6%

      \[\leadsto \frac{x}{e^{\color{blue}{a \cdot b}}} \]

   8. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + b \cdot \left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)\right)}\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(b \cdot \left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \color{blue}{\left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \color{blue}{\left(\frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right)\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(\left(\frac{1}{2} \cdot {a}^{2}\right) \cdot \color{blue}{b}\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\left(\frac{1}{2} \cdot {a}^{2}\right), \color{blue}{b}\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left({a}^{2}\right)\right), b\right)\right)\right)\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left(a \cdot a\right)\right), b\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 28.4%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(a, a\right)\right), b\right)\right)\right)\right)\right) \]

   10. Simplified 28.4%

       \[\leadsto \frac{x}{\color{blue}{1 + b \cdot \left(a + \left(0.5 \cdot \left(a \cdot a\right)\right) \cdot b\right)}} \]
   11. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(b \cdot \color{blue}{\left(\frac{1}{2} \cdot \left(a \cdot a\right)\right)}\right)\right)\right)\right)\right) \]

       2. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(b \cdot \left(\left(\frac{1}{2} \cdot a\right) \cdot \color{blue}{a}\right)\right)\right)\right)\right)\right) \]

       3. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(\left(b \cdot \left(\frac{1}{2} \cdot a\right)\right) \cdot \color{blue}{a}\right)\right)\right)\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\left(b \cdot \left(\frac{1}{2} \cdot a\right)\right), \color{blue}{a}\right)\right)\right)\right)\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \left(\frac{1}{2} \cdot a\right)\right), a\right)\right)\right)\right)\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \left(a \cdot \frac{1}{2}\right)\right), a\right)\right)\right)\right)\right) \]

       7. *-lowering-*.f64 23.2%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \frac{1}{2}\right)\right), a\right)\right)\right)\right)\right) \]

   12. Applied egg-rr 23.2%

       \[\leadsto \frac{x}{1 + b \cdot \left(a + \color{blue}{\left(b \cdot \left(a \cdot 0.5\right)\right) \cdot a}\right)} \]

   13. Taylor expanded in b around inf

       \[\leadsto \color{blue}{2 \cdot \frac{x}{{a}^{2} \cdot {b}^{2}}} \]
   14. Step-by-step derivation

       1. associate-/r* N/A

          \[\leadsto 2 \cdot \frac{\frac{x}{{a}^{2}}}{\color{blue}{{b}^{2}}} \]

       2. associate-*r/ N/A

          \[\leadsto \frac{2 \cdot \frac{x}{{a}^{2}}}{\color{blue}{{b}^{2}}} \]

       3. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left(2 \cdot \frac{x}{{a}^{2}}\right), \color{blue}{\left({b}^{2}\right)}\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(2, \left(\frac{x}{{a}^{2}}\right)\right), \left({\color{blue}{b}}^{2}\right)\right) \]

       5. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(2, \mathsf{/.f64}\left(x, \left({a}^{2}\right)\right)\right), \left({b}^{2}\right)\right) \]

       6. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(2, \mathsf{/.f64}\left(x, \left(a \cdot a\right)\right)\right), \left({b}^{2}\right)\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(2, \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, a\right)\right)\right), \left({b}^{2}\right)\right) \]

       8. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(2, \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, a\right)\right)\right), \left(b \cdot \color{blue}{b}\right)\right) \]

       9. *-lowering-*.f64 52.3%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(2, \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, a\right)\right)\right), \mathsf{*.f64}\left(b, \color{blue}{b}\right)\right) \]

   15. Simplified 52.3%

       \[\leadsto \color{blue}{\frac{2 \cdot \frac{x}{a \cdot a}}{b \cdot b}} \]

   if -1.25e-59 < y < 2.5000000000000001e-143

   1. Initial program 92.9%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 92.9%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(a \cdot b\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 82.9%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, b\right)\right)\right) \]

   7. Simplified 82.9%

      \[\leadsto \frac{x}{e^{\color{blue}{a \cdot b}}} \]

   8. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + b \cdot \left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)\right)}\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(b \cdot \left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \color{blue}{\left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \color{blue}{\left(\frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right)\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(\left(\frac{1}{2} \cdot {a}^{2}\right) \cdot \color{blue}{b}\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\left(\frac{1}{2} \cdot {a}^{2}\right), \color{blue}{b}\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left({a}^{2}\right)\right), b\right)\right)\right)\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left(a \cdot a\right)\right), b\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 55.3%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(a, a\right)\right), b\right)\right)\right)\right)\right) \]

   10. Simplified 55.3%

       \[\leadsto \frac{x}{\color{blue}{1 + b \cdot \left(a + \left(0.5 \cdot \left(a \cdot a\right)\right) \cdot b\right)}} \]

   11. Taylor expanded in b around 0

       \[\leadsto \color{blue}{x + -1 \cdot \left(a \cdot \left(b \cdot x\right)\right)} \]
   12. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto x + \left(\mathsf{neg}\left(a \cdot \left(b \cdot x\right)\right)\right) \]

       2. unsub-neg N/A

          \[\leadsto x - \color{blue}{a \cdot \left(b \cdot x\right)} \]

       3. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(a \cdot \left(b \cdot x\right)\right)}\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(a, \color{blue}{\left(b \cdot x\right)}\right)\right) \]

       5. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(a, \left(x \cdot \color{blue}{b}\right)\right)\right) \]

       6. *-lowering-*.f64 43.7%

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(x, \color{blue}{b}\right)\right)\right) \]

   13. Simplified 43.7%

       \[\leadsto \color{blue}{x - a \cdot \left(x \cdot b\right)} \]
   14. Step-by-step derivation

       1. associate-*r* N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \left(\left(a \cdot x\right) \cdot \color{blue}{b}\right)\right) \]

       2. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\left(a \cdot x\right), \color{blue}{b}\right)\right) \]

       3. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\left(x \cdot a\right), b\right)\right) \]

       4. *-lowering-*.f64 48.7%

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, a\right), b\right)\right) \]

   15. Applied egg-rr 48.7%

       \[\leadsto x - \color{blue}{\left(x \cdot a\right) \cdot b} \]

   if 2.5000000000000001e-143 < y < 3.9999999999999998e-7

   1. Initial program 96.6%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 96.6%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(t \cdot y\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\left(y \cdot t\right)\right)\right) \]

      2. *-lowering-*.f64 68.6%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, t\right)\right)\right) \]

   7. Simplified 68.6%

      \[\leadsto \frac{x}{e^{\color{blue}{y \cdot t}}} \]

   8. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x + y \cdot \left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) - t \cdot x\right)} \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot \left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) - t \cdot x\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) - t \cdot x\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right)\right), \color{blue}{\left(t \cdot x\right)}\right)\right)\right) \]

   10. Simplified 58.5%

       \[\leadsto \color{blue}{x + y \cdot \left(y \cdot \left(0.5 \cdot \left(x \cdot \left(t \cdot t\right)\right)\right) - x \cdot t\right)} \]

   11. Taylor expanded in x around 0

       \[\leadsto \color{blue}{x \cdot \left(1 + y \cdot \left(\frac{1}{2} \cdot \left({t}^{2} \cdot y\right) - t\right)\right)} \]
   12. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + y \cdot \left(\frac{1}{2} \cdot \left({t}^{2} \cdot y\right) - t\right)\right)}\right) \]

       2. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(y \cdot \left(\frac{1}{2} \cdot \left({t}^{2} \cdot y\right) - t\right)\right)}\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{1}{2} \cdot \left({t}^{2} \cdot y\right) - t\right)}\right)\right)\right) \]

       4. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\left(\frac{1}{2} \cdot \left({t}^{2} \cdot y\right)\right), \color{blue}{t}\right)\right)\right)\right) \]

       5. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\left(\left(\frac{1}{2} \cdot {t}^{2}\right) \cdot y\right), t\right)\right)\right)\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\left(\frac{1}{2} \cdot {t}^{2}\right), y\right), t\right)\right)\right)\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left({t}^{2}\right)\right), y\right), t\right)\right)\right)\right) \]

       8. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left(t \cdot t\right)\right), y\right), t\right)\right)\right)\right) \]

       9. *-lowering-*.f64 61.9%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(t, t\right)\right), y\right), t\right)\right)\right)\right) \]

   13. Simplified 61.9%

       \[\leadsto \color{blue}{x \cdot \left(1 + y \cdot \left(\left(0.5 \cdot \left(t \cdot t\right)\right) \cdot y - t\right)\right)} \]

   if 3.9999999999999998e-7 < y

   1. Initial program 98.2%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 98.2%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(t \cdot y\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\left(y \cdot t\right)\right)\right) \]

      2. *-lowering-*.f64 58.3%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, t\right)\right)\right) \]

   7. Simplified 58.3%

      \[\leadsto \frac{x}{e^{\color{blue}{y \cdot t}}} \]

   8. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x + y \cdot \left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) - t \cdot x\right)} \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot \left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) - t \cdot x\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) - t \cdot x\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right)\right), \color{blue}{\left(t \cdot x\right)}\right)\right)\right) \]

   10. Simplified 25.3%

       \[\leadsto \color{blue}{x + y \cdot \left(y \cdot \left(0.5 \cdot \left(x \cdot \left(t \cdot t\right)\right)\right) - x \cdot t\right)} \]

   11. Taylor expanded in y around inf

       \[\leadsto \color{blue}{\frac{1}{2} \cdot \left({t}^{2} \cdot \left(x \cdot {y}^{2}\right)\right)} \]
   12. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \left({t}^{2} \cdot \left(x \cdot {y}^{2}\right)\right) \cdot \color{blue}{\frac{1}{2}} \]

       2. *-commutative N/A

          \[\leadsto \left(\left(x \cdot {y}^{2}\right) \cdot {t}^{2}\right) \cdot \frac{1}{2} \]

       3. *-commutative N/A

          \[\leadsto \left(\left({y}^{2} \cdot x\right) \cdot {t}^{2}\right) \cdot \frac{1}{2} \]

       4. associate-*l* N/A

          \[\leadsto \left({y}^{2} \cdot \left(x \cdot {t}^{2}\right)\right) \cdot \frac{1}{2} \]

       5. *-commutative N/A

          \[\leadsto \left({y}^{2} \cdot \left({t}^{2} \cdot x\right)\right) \cdot \frac{1}{2} \]

       6. associate-*r* N/A

          \[\leadsto {y}^{2} \cdot \color{blue}{\left(\left({t}^{2} \cdot x\right) \cdot \frac{1}{2}\right)} \]

       7. *-commutative N/A

          \[\leadsto {y}^{2} \cdot \left(\frac{1}{2} \cdot \color{blue}{\left({t}^{2} \cdot x\right)}\right) \]

       8. unpow2 N/A

          \[\leadsto \left(y \cdot y\right) \cdot \left(\color{blue}{\frac{1}{2}} \cdot \left({t}^{2} \cdot x\right)\right) \]

       9. associate-*l* N/A

          \[\leadsto y \cdot \color{blue}{\left(y \cdot \left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right)} \]

       10. *-commutative N/A

           \[\leadsto y \cdot \left(y \cdot \left(\left({t}^{2} \cdot x\right) \cdot \color{blue}{\frac{1}{2}}\right)\right) \]

       11. associate-*r* N/A

           \[\leadsto y \cdot \left(\left(y \cdot \left({t}^{2} \cdot x\right)\right) \cdot \color{blue}{\frac{1}{2}}\right) \]

       12. *-commutative N/A

           \[\leadsto y \cdot \left(\left(y \cdot \left(x \cdot {t}^{2}\right)\right) \cdot \frac{1}{2}\right) \]

       13. associate-*l* N/A

           \[\leadsto y \cdot \left(\left(\left(y \cdot x\right) \cdot {t}^{2}\right) \cdot \frac{1}{2}\right) \]

       14. *-commutative N/A

           \[\leadsto y \cdot \left(\left(\left(x \cdot y\right) \cdot {t}^{2}\right) \cdot \frac{1}{2}\right) \]

       15. *-commutative N/A

           \[\leadsto y \cdot \left(\left({t}^{2} \cdot \left(x \cdot y\right)\right) \cdot \frac{1}{2}\right) \]

       16. *-commutative N/A

           \[\leadsto y \cdot \left(\frac{1}{2} \cdot \color{blue}{\left({t}^{2} \cdot \left(x \cdot y\right)\right)}\right) \]

       17. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{1}{2} \cdot \left({t}^{2} \cdot \left(x \cdot y\right)\right)\right)}\right) \]

       18. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{\left({t}^{2} \cdot \left(x \cdot y\right)\right)}\right)\right) \]

       19. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(\frac{1}{2}, \left(\left(x \cdot y\right) \cdot \color{blue}{{t}^{2}}\right)\right)\right) \]

       20. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(\frac{1}{2}, \left(\left(y \cdot x\right) \cdot {\color{blue}{t}}^{2}\right)\right)\right) \]

       21. associate-*l* N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(\frac{1}{2}, \left(y \cdot \color{blue}{\left(x \cdot {t}^{2}\right)}\right)\right)\right) \]

   13. Simplified 52.7%

       \[\leadsto \color{blue}{y \cdot \left(0.5 \cdot \left(y \cdot \left(x \cdot \left(t \cdot t\right)\right)\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 52.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+241}:\\ \;\;\;\;\frac{x}{0.5 \cdot \left(a \cdot \left(a \cdot \left(b \cdot b\right)\right)\right)}\\ \mathbf{elif}\;y \leq -3 \cdot 10^{+102}:\\ \;\;\;\;\frac{x}{y \cdot t + 1}\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{-59}:\\ \;\;\;\;\frac{2 \cdot \frac{x}{a \cdot a}}{b \cdot b}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-143}:\\ \;\;\;\;x - b \cdot \left(x \cdot a\right)\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-7}:\\ \;\;\;\;x \cdot \left(y \cdot \left(y \cdot \left(\left(t \cdot t\right) \cdot 0.5\right) - t\right) + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(0.5 \cdot \left(y \cdot \left(x \cdot \left(t \cdot t\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 42.1% accurate, 8.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+241}:\\ \;\;\;\;\frac{x}{0.5 \cdot \left(a \cdot \left(a \cdot \left(b \cdot b\right)\right)\right)}\\ \mathbf{elif}\;y \leq -3 \cdot 10^{+102}:\\ \;\;\;\;\frac{x}{y \cdot t + 1}\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{-60}:\\ \;\;\;\;\frac{2 \cdot \frac{x}{a \cdot a}}{b \cdot b}\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{-133}:\\ \;\;\;\;x - b \cdot \left(x \cdot a\right)\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{-32}:\\ \;\;\;\;\left(y \cdot y\right) \cdot \frac{x}{y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(0.5 \cdot \left(y \cdot \left(x \cdot \left(t \cdot t\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -8.5e+241)
   (/ x (* 0.5 (* a (* a (* b b)))))
   (if (<= y -3e+102)
     (/ x (+ (* y t) 1.0))
     (if (<= y -4.5e-60)
       (/ (* 2.0 (/ x (* a a))) (* b b))
       (if (<= y 1.75e-133)
         (- x (* b (* x a)))
         (if (<= y 2.15e-32)
           (* (* y y) (/ x (* y y)))
           (* y (* 0.5 (* y (* x (* t t)))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -8.5e+241) {
		tmp = x / (0.5 * (a * (a * (b * b))));
	} else if (y <= -3e+102) {
		tmp = x / ((y * t) + 1.0);
	} else if (y <= -4.5e-60) {
		tmp = (2.0 * (x / (a * a))) / (b * b);
	} else if (y <= 1.75e-133) {
		tmp = x - (b * (x * a));
	} else if (y <= 2.15e-32) {
		tmp = (y * y) * (x / (y * y));
	} else {
		tmp = y * (0.5 * (y * (x * (t * t))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-8.5d+241)) then
        tmp = x / (0.5d0 * (a * (a * (b * b))))
    else if (y <= (-3d+102)) then
        tmp = x / ((y * t) + 1.0d0)
    else if (y <= (-4.5d-60)) then
        tmp = (2.0d0 * (x / (a * a))) / (b * b)
    else if (y <= 1.75d-133) then
        tmp = x - (b * (x * a))
    else if (y <= 2.15d-32) then
        tmp = (y * y) * (x / (y * y))
    else
        tmp = y * (0.5d0 * (y * (x * (t * t))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -8.5e+241) {
		tmp = x / (0.5 * (a * (a * (b * b))));
	} else if (y <= -3e+102) {
		tmp = x / ((y * t) + 1.0);
	} else if (y <= -4.5e-60) {
		tmp = (2.0 * (x / (a * a))) / (b * b);
	} else if (y <= 1.75e-133) {
		tmp = x - (b * (x * a));
	} else if (y <= 2.15e-32) {
		tmp = (y * y) * (x / (y * y));
	} else {
		tmp = y * (0.5 * (y * (x * (t * t))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -8.5e+241:
		tmp = x / (0.5 * (a * (a * (b * b))))
	elif y <= -3e+102:
		tmp = x / ((y * t) + 1.0)
	elif y <= -4.5e-60:
		tmp = (2.0 * (x / (a * a))) / (b * b)
	elif y <= 1.75e-133:
		tmp = x - (b * (x * a))
	elif y <= 2.15e-32:
		tmp = (y * y) * (x / (y * y))
	else:
		tmp = y * (0.5 * (y * (x * (t * t))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -8.5e+241)
		tmp = Float64(x / Float64(0.5 * Float64(a * Float64(a * Float64(b * b)))));
	elseif (y <= -3e+102)
		tmp = Float64(x / Float64(Float64(y * t) + 1.0));
	elseif (y <= -4.5e-60)
		tmp = Float64(Float64(2.0 * Float64(x / Float64(a * a))) / Float64(b * b));
	elseif (y <= 1.75e-133)
		tmp = Float64(x - Float64(b * Float64(x * a)));
	elseif (y <= 2.15e-32)
		tmp = Float64(Float64(y * y) * Float64(x / Float64(y * y)));
	else
		tmp = Float64(y * Float64(0.5 * Float64(y * Float64(x * Float64(t * t)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -8.5e+241)
		tmp = x / (0.5 * (a * (a * (b * b))));
	elseif (y <= -3e+102)
		tmp = x / ((y * t) + 1.0);
	elseif (y <= -4.5e-60)
		tmp = (2.0 * (x / (a * a))) / (b * b);
	elseif (y <= 1.75e-133)
		tmp = x - (b * (x * a));
	elseif (y <= 2.15e-32)
		tmp = (y * y) * (x / (y * y));
	else
		tmp = y * (0.5 * (y * (x * (t * t))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -8.5e+241], N[(x / N[(0.5 * N[(a * N[(a * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3e+102], N[(x / N[(N[(y * t), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.5e-60], N[(N[(2.0 * N[(x / N[(a * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(b * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.75e-133], N[(x - N[(b * N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.15e-32], N[(N[(y * y), $MachinePrecision] * N[(x / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(0.5 * N[(y * N[(x * N[(t * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -8.49999999999999954e241

   1. Initial program 100.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(a \cdot b\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 14.7%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, b\right)\right)\right) \]

   7. Simplified 14.7%

      \[\leadsto \frac{x}{e^{\color{blue}{a \cdot b}}} \]

   8. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + b \cdot \left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)\right)}\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(b \cdot \left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \color{blue}{\left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \color{blue}{\left(\frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right)\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(\left(\frac{1}{2} \cdot {a}^{2}\right) \cdot \color{blue}{b}\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\left(\frac{1}{2} \cdot {a}^{2}\right), \color{blue}{b}\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left({a}^{2}\right)\right), b\right)\right)\right)\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left(a \cdot a\right)\right), b\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 3.5%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(a, a\right)\right), b\right)\right)\right)\right)\right) \]

   10. Simplified 3.5%

       \[\leadsto \frac{x}{\color{blue}{1 + b \cdot \left(a + \left(0.5 \cdot \left(a \cdot a\right)\right) \cdot b\right)}} \]
   11. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(b \cdot \color{blue}{\left(\frac{1}{2} \cdot \left(a \cdot a\right)\right)}\right)\right)\right)\right)\right) \]

       2. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(b \cdot \left(\left(\frac{1}{2} \cdot a\right) \cdot \color{blue}{a}\right)\right)\right)\right)\right)\right) \]

       3. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(\left(b \cdot \left(\frac{1}{2} \cdot a\right)\right) \cdot \color{blue}{a}\right)\right)\right)\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\left(b \cdot \left(\frac{1}{2} \cdot a\right)\right), \color{blue}{a}\right)\right)\right)\right)\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \left(\frac{1}{2} \cdot a\right)\right), a\right)\right)\right)\right)\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \left(a \cdot \frac{1}{2}\right)\right), a\right)\right)\right)\right)\right) \]

       7. *-lowering-*.f64 3.8%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \frac{1}{2}\right)\right), a\right)\right)\right)\right)\right) \]

   12. Applied egg-rr 3.8%

       \[\leadsto \frac{x}{1 + b \cdot \left(a + \color{blue}{\left(b \cdot \left(a \cdot 0.5\right)\right) \cdot a}\right)} \]

   13. Taylor expanded in b around inf

       \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(\frac{1}{2} \cdot \left({a}^{2} \cdot {b}^{2}\right)\right)}\right) \]
   14. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{\left({a}^{2} \cdot {b}^{2}\right)}\right)\right) \]

       2. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{2}, \left(\left(a \cdot a\right) \cdot {\color{blue}{b}}^{2}\right)\right)\right) \]

       3. associate-*l* N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{2}, \left(a \cdot \color{blue}{\left(a \cdot {b}^{2}\right)}\right)\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(a, \color{blue}{\left(a \cdot {b}^{2}\right)}\right)\right)\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(a, \color{blue}{\left({b}^{2}\right)}\right)\right)\right)\right) \]

       6. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(a, \left(b \cdot \color{blue}{b}\right)\right)\right)\right)\right) \]

       7. *-lowering-*.f64 54.4%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(b, \color{blue}{b}\right)\right)\right)\right)\right) \]

   15. Simplified 54.4%

       \[\leadsto \frac{x}{\color{blue}{0.5 \cdot \left(a \cdot \left(a \cdot \left(b \cdot b\right)\right)\right)}} \]

   if -8.49999999999999954e241 < y < -2.9999999999999998e102

   1. Initial program 100.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(t \cdot y\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\left(y \cdot t\right)\right)\right) \]

      2. *-lowering-*.f64 90.8%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, t\right)\right)\right) \]

   7. Simplified 90.8%

      \[\leadsto \frac{x}{e^{\color{blue}{y \cdot t}}} \]

   8. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + t \cdot y\right)}\right) \]
   9. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(t \cdot y + \color{blue}{1}\right)\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\left(t \cdot y\right), \color{blue}{1}\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\left(y \cdot t\right), 1\right)\right) \]

      4. *-lowering-*.f64 53.7%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, t\right), 1\right)\right) \]

   10. Simplified 53.7%

       \[\leadsto \frac{x}{\color{blue}{y \cdot t + 1}} \]

   if -2.9999999999999998e102 < y < -4.50000000000000001e-60

   1. Initial program 97.3%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 97.3%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(a \cdot b\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 49.6%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, b\right)\right)\right) \]

   7. Simplified 49.6%

      \[\leadsto \frac{x}{e^{\color{blue}{a \cdot b}}} \]

   8. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + b \cdot \left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)\right)}\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(b \cdot \left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \color{blue}{\left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \color{blue}{\left(\frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right)\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(\left(\frac{1}{2} \cdot {a}^{2}\right) \cdot \color{blue}{b}\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\left(\frac{1}{2} \cdot {a}^{2}\right), \color{blue}{b}\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left({a}^{2}\right)\right), b\right)\right)\right)\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left(a \cdot a\right)\right), b\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 28.4%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(a, a\right)\right), b\right)\right)\right)\right)\right) \]

   10. Simplified 28.4%

       \[\leadsto \frac{x}{\color{blue}{1 + b \cdot \left(a + \left(0.5 \cdot \left(a \cdot a\right)\right) \cdot b\right)}} \]
   11. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(b \cdot \color{blue}{\left(\frac{1}{2} \cdot \left(a \cdot a\right)\right)}\right)\right)\right)\right)\right) \]

       2. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(b \cdot \left(\left(\frac{1}{2} \cdot a\right) \cdot \color{blue}{a}\right)\right)\right)\right)\right)\right) \]

       3. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(\left(b \cdot \left(\frac{1}{2} \cdot a\right)\right) \cdot \color{blue}{a}\right)\right)\right)\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\left(b \cdot \left(\frac{1}{2} \cdot a\right)\right), \color{blue}{a}\right)\right)\right)\right)\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \left(\frac{1}{2} \cdot a\right)\right), a\right)\right)\right)\right)\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \left(a \cdot \frac{1}{2}\right)\right), a\right)\right)\right)\right)\right) \]

       7. *-lowering-*.f64 23.2%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \frac{1}{2}\right)\right), a\right)\right)\right)\right)\right) \]

   12. Applied egg-rr 23.2%

       \[\leadsto \frac{x}{1 + b \cdot \left(a + \color{blue}{\left(b \cdot \left(a \cdot 0.5\right)\right) \cdot a}\right)} \]

   13. Taylor expanded in b around inf

       \[\leadsto \color{blue}{2 \cdot \frac{x}{{a}^{2} \cdot {b}^{2}}} \]
   14. Step-by-step derivation

       1. associate-/r* N/A

          \[\leadsto 2 \cdot \frac{\frac{x}{{a}^{2}}}{\color{blue}{{b}^{2}}} \]

       2. associate-*r/ N/A

          \[\leadsto \frac{2 \cdot \frac{x}{{a}^{2}}}{\color{blue}{{b}^{2}}} \]

       3. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left(2 \cdot \frac{x}{{a}^{2}}\right), \color{blue}{\left({b}^{2}\right)}\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(2, \left(\frac{x}{{a}^{2}}\right)\right), \left({\color{blue}{b}}^{2}\right)\right) \]

       5. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(2, \mathsf{/.f64}\left(x, \left({a}^{2}\right)\right)\right), \left({b}^{2}\right)\right) \]

       6. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(2, \mathsf{/.f64}\left(x, \left(a \cdot a\right)\right)\right), \left({b}^{2}\right)\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(2, \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, a\right)\right)\right), \left({b}^{2}\right)\right) \]

       8. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(2, \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, a\right)\right)\right), \left(b \cdot \color{blue}{b}\right)\right) \]

       9. *-lowering-*.f64 52.3%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(2, \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, a\right)\right)\right), \mathsf{*.f64}\left(b, \color{blue}{b}\right)\right) \]

   15. Simplified 52.3%

       \[\leadsto \color{blue}{\frac{2 \cdot \frac{x}{a \cdot a}}{b \cdot b}} \]

   if -4.50000000000000001e-60 < y < 1.75000000000000001e-133

   1. Initial program 93.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 93.0%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(a \cdot b\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 83.3%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, b\right)\right)\right) \]

   7. Simplified 83.3%

      \[\leadsto \frac{x}{e^{\color{blue}{a \cdot b}}} \]

   8. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + b \cdot \left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)\right)}\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(b \cdot \left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \color{blue}{\left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \color{blue}{\left(\frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right)\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(\left(\frac{1}{2} \cdot {a}^{2}\right) \cdot \color{blue}{b}\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\left(\frac{1}{2} \cdot {a}^{2}\right), \color{blue}{b}\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left({a}^{2}\right)\right), b\right)\right)\right)\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left(a \cdot a\right)\right), b\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 56.2%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(a, a\right)\right), b\right)\right)\right)\right)\right) \]

   10. Simplified 56.2%

       \[\leadsto \frac{x}{\color{blue}{1 + b \cdot \left(a + \left(0.5 \cdot \left(a \cdot a\right)\right) \cdot b\right)}} \]

   11. Taylor expanded in b around 0

       \[\leadsto \color{blue}{x + -1 \cdot \left(a \cdot \left(b \cdot x\right)\right)} \]
   12. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto x + \left(\mathsf{neg}\left(a \cdot \left(b \cdot x\right)\right)\right) \]

       2. unsub-neg N/A

          \[\leadsto x - \color{blue}{a \cdot \left(b \cdot x\right)} \]

       3. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(a \cdot \left(b \cdot x\right)\right)}\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(a, \color{blue}{\left(b \cdot x\right)}\right)\right) \]

       5. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(a, \left(x \cdot \color{blue}{b}\right)\right)\right) \]

       6. *-lowering-*.f64 44.9%

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(x, \color{blue}{b}\right)\right)\right) \]

   13. Simplified 44.9%

       \[\leadsto \color{blue}{x - a \cdot \left(x \cdot b\right)} \]
   14. Step-by-step derivation

       1. associate-*r* N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \left(\left(a \cdot x\right) \cdot \color{blue}{b}\right)\right) \]

       2. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\left(a \cdot x\right), \color{blue}{b}\right)\right) \]

       3. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\left(x \cdot a\right), b\right)\right) \]

       4. *-lowering-*.f64 49.7%

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, a\right), b\right)\right) \]

   15. Applied egg-rr 49.7%

       \[\leadsto x - \color{blue}{\left(x \cdot a\right) \cdot b} \]

   if 1.75000000000000001e-133 < y < 2.14999999999999995e-32

   1. Initial program 100.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(t \cdot y\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\left(y \cdot t\right)\right)\right) \]

      2. *-lowering-*.f64 71.8%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, t\right)\right)\right) \]

   7. Simplified 71.8%

      \[\leadsto \frac{x}{e^{\color{blue}{y \cdot t}}} \]

   8. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x + y \cdot \left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) - t \cdot x\right)} \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot \left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) - t \cdot x\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) - t \cdot x\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right)\right), \color{blue}{\left(t \cdot x\right)}\right)\right)\right) \]

   10. Simplified 58.3%

       \[\leadsto \color{blue}{x + y \cdot \left(y \cdot \left(0.5 \cdot \left(x \cdot \left(t \cdot t\right)\right)\right) - x \cdot t\right)} \]

   11. Taylor expanded in y around -inf

       \[\leadsto \color{blue}{{y}^{2} \cdot \left(-1 \cdot \frac{-1 \cdot \frac{x}{y} + t \cdot x}{y} + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)} \]
   12. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left({y}^{2}\right), \color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{x}{y} + t \cdot x}{y} + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)}\right) \]

       2. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(y \cdot y\right), \left(\color{blue}{-1 \cdot \frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}} + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \left(\color{blue}{-1 \cdot \frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}} + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) \]

       4. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right) + \color{blue}{-1 \cdot \frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}}\right)\right) \]

       5. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right) + \left(\mathsf{neg}\left(\frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}\right)\right)\right)\right) \]

       6. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right) - \color{blue}{\frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}}\right)\right) \]

       7. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right), \color{blue}{\left(\frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}\right)}\right)\right) \]

       8. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\left(\left({t}^{2} \cdot x\right) \cdot \frac{1}{2}\right), \left(\frac{\color{blue}{-1 \cdot \frac{x}{y} + t \cdot x}}{y}\right)\right)\right) \]

       9. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\left(\left(x \cdot {t}^{2}\right) \cdot \frac{1}{2}\right), \left(\frac{\color{blue}{-1 \cdot \frac{x}{y}} + t \cdot x}{y}\right)\right)\right) \]

       10. associate-*l* N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\left(x \cdot \left({t}^{2} \cdot \frac{1}{2}\right)\right), \left(\frac{\color{blue}{-1 \cdot \frac{x}{y} + t \cdot x}}{y}\right)\right)\right) \]

       11. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \left({t}^{2} \cdot \frac{1}{2}\right)\right), \left(\frac{\color{blue}{-1 \cdot \frac{x}{y} + t \cdot x}}{y}\right)\right)\right) \]

       12. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\left({t}^{2}\right), \frac{1}{2}\right)\right), \left(\frac{-1 \cdot \frac{x}{y} + \color{blue}{t \cdot x}}{y}\right)\right)\right) \]

       13. unpow2 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\left(t \cdot t\right), \frac{1}{2}\right)\right), \left(\frac{-1 \cdot \frac{x}{y} + \color{blue}{t} \cdot x}{y}\right)\right)\right) \]

       14. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, t\right), \frac{1}{2}\right)\right), \left(\frac{-1 \cdot \frac{x}{y} + \color{blue}{t} \cdot x}{y}\right)\right)\right) \]

       15. /-lowering-/.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, t\right), \frac{1}{2}\right)\right), \mathsf{/.f64}\left(\left(-1 \cdot \frac{x}{y} + t \cdot x\right), \color{blue}{y}\right)\right)\right) \]

   13. Simplified 66.6%

       \[\leadsto \color{blue}{\left(y \cdot y\right) \cdot \left(x \cdot \left(\left(t \cdot t\right) \cdot 0.5\right) - \frac{x \cdot t - \frac{x}{y}}{y}\right)} \]

   14. Taylor expanded in t around 0

       \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \color{blue}{\left(\frac{x}{{y}^{2}}\right)}\right) \]
   15. Step-by-step derivation

       1. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{/.f64}\left(x, \color{blue}{\left({y}^{2}\right)}\right)\right) \]

       2. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{/.f64}\left(x, \left(y \cdot \color{blue}{y}\right)\right)\right) \]

       3. *-lowering-*.f64 62.6%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{y}\right)\right)\right) \]

   16. Simplified 62.6%

       \[\leadsto \left(y \cdot y\right) \cdot \color{blue}{\frac{x}{y \cdot y}} \]

   if 2.14999999999999995e-32 < y

   1. Initial program 96.7%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 96.8%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(t \cdot y\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\left(y \cdot t\right)\right)\right) \]

      2. *-lowering-*.f64 57.0%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, t\right)\right)\right) \]

   7. Simplified 57.0%

      \[\leadsto \frac{x}{e^{\color{blue}{y \cdot t}}} \]

   8. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x + y \cdot \left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) - t \cdot x\right)} \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot \left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) - t \cdot x\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) - t \cdot x\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right)\right), \color{blue}{\left(t \cdot x\right)}\right)\right)\right) \]

   10. Simplified 28.3%

       \[\leadsto \color{blue}{x + y \cdot \left(y \cdot \left(0.5 \cdot \left(x \cdot \left(t \cdot t\right)\right)\right) - x \cdot t\right)} \]

   11. Taylor expanded in y around inf

       \[\leadsto \color{blue}{\frac{1}{2} \cdot \left({t}^{2} \cdot \left(x \cdot {y}^{2}\right)\right)} \]
   12. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \left({t}^{2} \cdot \left(x \cdot {y}^{2}\right)\right) \cdot \color{blue}{\frac{1}{2}} \]

       2. *-commutative N/A

          \[\leadsto \left(\left(x \cdot {y}^{2}\right) \cdot {t}^{2}\right) \cdot \frac{1}{2} \]

       3. *-commutative N/A

          \[\leadsto \left(\left({y}^{2} \cdot x\right) \cdot {t}^{2}\right) \cdot \frac{1}{2} \]

       4. associate-*l* N/A

          \[\leadsto \left({y}^{2} \cdot \left(x \cdot {t}^{2}\right)\right) \cdot \frac{1}{2} \]

       5. *-commutative N/A

          \[\leadsto \left({y}^{2} \cdot \left({t}^{2} \cdot x\right)\right) \cdot \frac{1}{2} \]

       6. associate-*r* N/A

          \[\leadsto {y}^{2} \cdot \color{blue}{\left(\left({t}^{2} \cdot x\right) \cdot \frac{1}{2}\right)} \]

       7. *-commutative N/A

          \[\leadsto {y}^{2} \cdot \left(\frac{1}{2} \cdot \color{blue}{\left({t}^{2} \cdot x\right)}\right) \]

       8. unpow2 N/A

          \[\leadsto \left(y \cdot y\right) \cdot \left(\color{blue}{\frac{1}{2}} \cdot \left({t}^{2} \cdot x\right)\right) \]

       9. associate-*l* N/A

          \[\leadsto y \cdot \color{blue}{\left(y \cdot \left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right)} \]

       10. *-commutative N/A

           \[\leadsto y \cdot \left(y \cdot \left(\left({t}^{2} \cdot x\right) \cdot \color{blue}{\frac{1}{2}}\right)\right) \]

       11. associate-*r* N/A

           \[\leadsto y \cdot \left(\left(y \cdot \left({t}^{2} \cdot x\right)\right) \cdot \color{blue}{\frac{1}{2}}\right) \]

       12. *-commutative N/A

           \[\leadsto y \cdot \left(\left(y \cdot \left(x \cdot {t}^{2}\right)\right) \cdot \frac{1}{2}\right) \]

       13. associate-*l* N/A

           \[\leadsto y \cdot \left(\left(\left(y \cdot x\right) \cdot {t}^{2}\right) \cdot \frac{1}{2}\right) \]

       14. *-commutative N/A

           \[\leadsto y \cdot \left(\left(\left(x \cdot y\right) \cdot {t}^{2}\right) \cdot \frac{1}{2}\right) \]

       15. *-commutative N/A

           \[\leadsto y \cdot \left(\left({t}^{2} \cdot \left(x \cdot y\right)\right) \cdot \frac{1}{2}\right) \]

       16. *-commutative N/A

           \[\leadsto y \cdot \left(\frac{1}{2} \cdot \color{blue}{\left({t}^{2} \cdot \left(x \cdot y\right)\right)}\right) \]

       17. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{1}{2} \cdot \left({t}^{2} \cdot \left(x \cdot y\right)\right)\right)}\right) \]

       18. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{\left({t}^{2} \cdot \left(x \cdot y\right)\right)}\right)\right) \]

       19. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(\frac{1}{2}, \left(\left(x \cdot y\right) \cdot \color{blue}{{t}^{2}}\right)\right)\right) \]

       20. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(\frac{1}{2}, \left(\left(y \cdot x\right) \cdot {\color{blue}{t}}^{2}\right)\right)\right) \]

       21. associate-*l* N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(\frac{1}{2}, \left(y \cdot \color{blue}{\left(x \cdot {t}^{2}\right)}\right)\right)\right) \]

   13. Simplified 51.8%

       \[\leadsto \color{blue}{y \cdot \left(0.5 \cdot \left(y \cdot \left(x \cdot \left(t \cdot t\right)\right)\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 52.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+241}:\\ \;\;\;\;\frac{x}{0.5 \cdot \left(a \cdot \left(a \cdot \left(b \cdot b\right)\right)\right)}\\ \mathbf{elif}\;y \leq -3 \cdot 10^{+102}:\\ \;\;\;\;\frac{x}{y \cdot t + 1}\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{-60}:\\ \;\;\;\;\frac{2 \cdot \frac{x}{a \cdot a}}{b \cdot b}\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{-133}:\\ \;\;\;\;x - b \cdot \left(x \cdot a\right)\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{-32}:\\ \;\;\;\;\left(y \cdot y\right) \cdot \frac{x}{y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(0.5 \cdot \left(y \cdot \left(x \cdot \left(t \cdot t\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 45.3% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+241}:\\ \;\;\;\;\frac{x}{0.5 \cdot \left(a \cdot \left(a \cdot \left(b \cdot b\right)\right)\right)}\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{+102}:\\ \;\;\;\;\frac{x}{y \cdot t + 1}\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-59}:\\ \;\;\;\;\frac{2 \cdot \frac{x}{a \cdot a}}{b \cdot b}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-8}:\\ \;\;\;\;x + b \cdot \left(a \cdot \left(0.5 \cdot \left(a \cdot \left(x \cdot b\right)\right) - x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(0.5 \cdot \left(y \cdot \left(x \cdot \left(t \cdot t\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -9e+241)
   (/ x (* 0.5 (* a (* a (* b b)))))
   (if (<= y -2.3e+102)
     (/ x (+ (* y t) 1.0))
     (if (<= y -1.35e-59)
       (/ (* 2.0 (/ x (* a a))) (* b b))
       (if (<= y 1.2e-8)
         (+ x (* b (* a (- (* 0.5 (* a (* x b))) x))))
         (* y (* 0.5 (* y (* x (* t t))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -9e+241) {
		tmp = x / (0.5 * (a * (a * (b * b))));
	} else if (y <= -2.3e+102) {
		tmp = x / ((y * t) + 1.0);
	} else if (y <= -1.35e-59) {
		tmp = (2.0 * (x / (a * a))) / (b * b);
	} else if (y <= 1.2e-8) {
		tmp = x + (b * (a * ((0.5 * (a * (x * b))) - x)));
	} else {
		tmp = y * (0.5 * (y * (x * (t * t))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-9d+241)) then
        tmp = x / (0.5d0 * (a * (a * (b * b))))
    else if (y <= (-2.3d+102)) then
        tmp = x / ((y * t) + 1.0d0)
    else if (y <= (-1.35d-59)) then
        tmp = (2.0d0 * (x / (a * a))) / (b * b)
    else if (y <= 1.2d-8) then
        tmp = x + (b * (a * ((0.5d0 * (a * (x * b))) - x)))
    else
        tmp = y * (0.5d0 * (y * (x * (t * t))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -9e+241) {
		tmp = x / (0.5 * (a * (a * (b * b))));
	} else if (y <= -2.3e+102) {
		tmp = x / ((y * t) + 1.0);
	} else if (y <= -1.35e-59) {
		tmp = (2.0 * (x / (a * a))) / (b * b);
	} else if (y <= 1.2e-8) {
		tmp = x + (b * (a * ((0.5 * (a * (x * b))) - x)));
	} else {
		tmp = y * (0.5 * (y * (x * (t * t))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -9e+241:
		tmp = x / (0.5 * (a * (a * (b * b))))
	elif y <= -2.3e+102:
		tmp = x / ((y * t) + 1.0)
	elif y <= -1.35e-59:
		tmp = (2.0 * (x / (a * a))) / (b * b)
	elif y <= 1.2e-8:
		tmp = x + (b * (a * ((0.5 * (a * (x * b))) - x)))
	else:
		tmp = y * (0.5 * (y * (x * (t * t))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -9e+241)
		tmp = Float64(x / Float64(0.5 * Float64(a * Float64(a * Float64(b * b)))));
	elseif (y <= -2.3e+102)
		tmp = Float64(x / Float64(Float64(y * t) + 1.0));
	elseif (y <= -1.35e-59)
		tmp = Float64(Float64(2.0 * Float64(x / Float64(a * a))) / Float64(b * b));
	elseif (y <= 1.2e-8)
		tmp = Float64(x + Float64(b * Float64(a * Float64(Float64(0.5 * Float64(a * Float64(x * b))) - x))));
	else
		tmp = Float64(y * Float64(0.5 * Float64(y * Float64(x * Float64(t * t)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -9e+241)
		tmp = x / (0.5 * (a * (a * (b * b))));
	elseif (y <= -2.3e+102)
		tmp = x / ((y * t) + 1.0);
	elseif (y <= -1.35e-59)
		tmp = (2.0 * (x / (a * a))) / (b * b);
	elseif (y <= 1.2e-8)
		tmp = x + (b * (a * ((0.5 * (a * (x * b))) - x)));
	else
		tmp = y * (0.5 * (y * (x * (t * t))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -9e+241], N[(x / N[(0.5 * N[(a * N[(a * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.3e+102], N[(x / N[(N[(y * t), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.35e-59], N[(N[(2.0 * N[(x / N[(a * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(b * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.2e-8], N[(x + N[(b * N[(a * N[(N[(0.5 * N[(a * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(0.5 * N[(y * N[(x * N[(t * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -8.99999999999999987e241

   1. Initial program 100.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(a \cdot b\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 14.7%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, b\right)\right)\right) \]

   7. Simplified 14.7%

      \[\leadsto \frac{x}{e^{\color{blue}{a \cdot b}}} \]

   8. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + b \cdot \left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)\right)}\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(b \cdot \left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \color{blue}{\left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \color{blue}{\left(\frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right)\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(\left(\frac{1}{2} \cdot {a}^{2}\right) \cdot \color{blue}{b}\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\left(\frac{1}{2} \cdot {a}^{2}\right), \color{blue}{b}\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left({a}^{2}\right)\right), b\right)\right)\right)\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left(a \cdot a\right)\right), b\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 3.5%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(a, a\right)\right), b\right)\right)\right)\right)\right) \]

   10. Simplified 3.5%

       \[\leadsto \frac{x}{\color{blue}{1 + b \cdot \left(a + \left(0.5 \cdot \left(a \cdot a\right)\right) \cdot b\right)}} \]
   11. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(b \cdot \color{blue}{\left(\frac{1}{2} \cdot \left(a \cdot a\right)\right)}\right)\right)\right)\right)\right) \]

       2. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(b \cdot \left(\left(\frac{1}{2} \cdot a\right) \cdot \color{blue}{a}\right)\right)\right)\right)\right)\right) \]

       3. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(\left(b \cdot \left(\frac{1}{2} \cdot a\right)\right) \cdot \color{blue}{a}\right)\right)\right)\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\left(b \cdot \left(\frac{1}{2} \cdot a\right)\right), \color{blue}{a}\right)\right)\right)\right)\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \left(\frac{1}{2} \cdot a\right)\right), a\right)\right)\right)\right)\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \left(a \cdot \frac{1}{2}\right)\right), a\right)\right)\right)\right)\right) \]

       7. *-lowering-*.f64 3.8%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \frac{1}{2}\right)\right), a\right)\right)\right)\right)\right) \]

   12. Applied egg-rr 3.8%

       \[\leadsto \frac{x}{1 + b \cdot \left(a + \color{blue}{\left(b \cdot \left(a \cdot 0.5\right)\right) \cdot a}\right)} \]

   13. Taylor expanded in b around inf

       \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(\frac{1}{2} \cdot \left({a}^{2} \cdot {b}^{2}\right)\right)}\right) \]
   14. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{\left({a}^{2} \cdot {b}^{2}\right)}\right)\right) \]

       2. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{2}, \left(\left(a \cdot a\right) \cdot {\color{blue}{b}}^{2}\right)\right)\right) \]

       3. associate-*l* N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{2}, \left(a \cdot \color{blue}{\left(a \cdot {b}^{2}\right)}\right)\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(a, \color{blue}{\left(a \cdot {b}^{2}\right)}\right)\right)\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(a, \color{blue}{\left({b}^{2}\right)}\right)\right)\right)\right) \]

       6. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(a, \left(b \cdot \color{blue}{b}\right)\right)\right)\right)\right) \]

       7. *-lowering-*.f64 54.4%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(b, \color{blue}{b}\right)\right)\right)\right)\right) \]

   15. Simplified 54.4%

       \[\leadsto \frac{x}{\color{blue}{0.5 \cdot \left(a \cdot \left(a \cdot \left(b \cdot b\right)\right)\right)}} \]

   if -8.99999999999999987e241 < y < -2.2999999999999999e102

   1. Initial program 100.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(t \cdot y\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\left(y \cdot t\right)\right)\right) \]

      2. *-lowering-*.f64 90.8%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, t\right)\right)\right) \]

   7. Simplified 90.8%

      \[\leadsto \frac{x}{e^{\color{blue}{y \cdot t}}} \]

   8. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + t \cdot y\right)}\right) \]
   9. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(t \cdot y + \color{blue}{1}\right)\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\left(t \cdot y\right), \color{blue}{1}\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\left(y \cdot t\right), 1\right)\right) \]

      4. *-lowering-*.f64 53.7%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, t\right), 1\right)\right) \]

   10. Simplified 53.7%

       \[\leadsto \frac{x}{\color{blue}{y \cdot t + 1}} \]

   if -2.2999999999999999e102 < y < -1.3499999999999999e-59

   1. Initial program 97.3%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 97.3%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(a \cdot b\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 49.6%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, b\right)\right)\right) \]

   7. Simplified 49.6%

      \[\leadsto \frac{x}{e^{\color{blue}{a \cdot b}}} \]

   8. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + b \cdot \left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)\right)}\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(b \cdot \left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \color{blue}{\left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \color{blue}{\left(\frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right)\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(\left(\frac{1}{2} \cdot {a}^{2}\right) \cdot \color{blue}{b}\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\left(\frac{1}{2} \cdot {a}^{2}\right), \color{blue}{b}\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left({a}^{2}\right)\right), b\right)\right)\right)\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left(a \cdot a\right)\right), b\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 28.4%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(a, a\right)\right), b\right)\right)\right)\right)\right) \]

   10. Simplified 28.4%

       \[\leadsto \frac{x}{\color{blue}{1 + b \cdot \left(a + \left(0.5 \cdot \left(a \cdot a\right)\right) \cdot b\right)}} \]
   11. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(b \cdot \color{blue}{\left(\frac{1}{2} \cdot \left(a \cdot a\right)\right)}\right)\right)\right)\right)\right) \]

       2. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(b \cdot \left(\left(\frac{1}{2} \cdot a\right) \cdot \color{blue}{a}\right)\right)\right)\right)\right)\right) \]

       3. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(\left(b \cdot \left(\frac{1}{2} \cdot a\right)\right) \cdot \color{blue}{a}\right)\right)\right)\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\left(b \cdot \left(\frac{1}{2} \cdot a\right)\right), \color{blue}{a}\right)\right)\right)\right)\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \left(\frac{1}{2} \cdot a\right)\right), a\right)\right)\right)\right)\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \left(a \cdot \frac{1}{2}\right)\right), a\right)\right)\right)\right)\right) \]

       7. *-lowering-*.f64 23.2%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \frac{1}{2}\right)\right), a\right)\right)\right)\right)\right) \]

   12. Applied egg-rr 23.2%

       \[\leadsto \frac{x}{1 + b \cdot \left(a + \color{blue}{\left(b \cdot \left(a \cdot 0.5\right)\right) \cdot a}\right)} \]

   13. Taylor expanded in b around inf

       \[\leadsto \color{blue}{2 \cdot \frac{x}{{a}^{2} \cdot {b}^{2}}} \]
   14. Step-by-step derivation

       1. associate-/r* N/A

          \[\leadsto 2 \cdot \frac{\frac{x}{{a}^{2}}}{\color{blue}{{b}^{2}}} \]

       2. associate-*r/ N/A

          \[\leadsto \frac{2 \cdot \frac{x}{{a}^{2}}}{\color{blue}{{b}^{2}}} \]

       3. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left(2 \cdot \frac{x}{{a}^{2}}\right), \color{blue}{\left({b}^{2}\right)}\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(2, \left(\frac{x}{{a}^{2}}\right)\right), \left({\color{blue}{b}}^{2}\right)\right) \]

       5. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(2, \mathsf{/.f64}\left(x, \left({a}^{2}\right)\right)\right), \left({b}^{2}\right)\right) \]

       6. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(2, \mathsf{/.f64}\left(x, \left(a \cdot a\right)\right)\right), \left({b}^{2}\right)\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(2, \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, a\right)\right)\right), \left({b}^{2}\right)\right) \]

       8. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(2, \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, a\right)\right)\right), \left(b \cdot \color{blue}{b}\right)\right) \]

       9. *-lowering-*.f64 52.3%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(2, \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(a, a\right)\right)\right), \mathsf{*.f64}\left(b, \color{blue}{b}\right)\right) \]

   15. Simplified 52.3%

       \[\leadsto \color{blue}{\frac{2 \cdot \frac{x}{a \cdot a}}{b \cdot b}} \]

   if -1.3499999999999999e-59 < y < 1.19999999999999999e-8

   1. Initial program 93.7%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 93.7%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(a \cdot b\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 78.4%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, b\right)\right)\right) \]

   7. Simplified 78.4%

      \[\leadsto \frac{x}{e^{\color{blue}{a \cdot b}}} \]

   8. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + b \cdot \left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)\right)}\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(b \cdot \left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \color{blue}{\left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \color{blue}{\left(\frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right)\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(\left(\frac{1}{2} \cdot {a}^{2}\right) \cdot \color{blue}{b}\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\left(\frac{1}{2} \cdot {a}^{2}\right), \color{blue}{b}\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left({a}^{2}\right)\right), b\right)\right)\right)\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left(a \cdot a\right)\right), b\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 50.2%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(a, a\right)\right), b\right)\right)\right)\right)\right) \]

   10. Simplified 50.2%

       \[\leadsto \frac{x}{\color{blue}{1 + b \cdot \left(a + \left(0.5 \cdot \left(a \cdot a\right)\right) \cdot b\right)}} \]

   11. Taylor expanded in b around 0

       \[\leadsto \color{blue}{x + b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left({a}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({a}^{2} \cdot x\right)\right)\right) - a \cdot x\right)} \]

   13. Simplified 54.4%

       \[\leadsto \color{blue}{x + b \cdot \left(a \cdot \left(0.5 \cdot \left(a \cdot \left(x \cdot b\right)\right) - x\right)\right)} \]

   if 1.19999999999999999e-8 < y

   1. Initial program 98.2%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 98.2%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(t \cdot y\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\left(y \cdot t\right)\right)\right) \]

      2. *-lowering-*.f64 58.3%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, t\right)\right)\right) \]

   7. Simplified 58.3%

      \[\leadsto \frac{x}{e^{\color{blue}{y \cdot t}}} \]

   8. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x + y \cdot \left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) - t \cdot x\right)} \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot \left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) - t \cdot x\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) - t \cdot x\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right)\right), \color{blue}{\left(t \cdot x\right)}\right)\right)\right) \]

   10. Simplified 25.3%

       \[\leadsto \color{blue}{x + y \cdot \left(y \cdot \left(0.5 \cdot \left(x \cdot \left(t \cdot t\right)\right)\right) - x \cdot t\right)} \]

   11. Taylor expanded in y around inf

       \[\leadsto \color{blue}{\frac{1}{2} \cdot \left({t}^{2} \cdot \left(x \cdot {y}^{2}\right)\right)} \]
   12. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \left({t}^{2} \cdot \left(x \cdot {y}^{2}\right)\right) \cdot \color{blue}{\frac{1}{2}} \]

       2. *-commutative N/A

          \[\leadsto \left(\left(x \cdot {y}^{2}\right) \cdot {t}^{2}\right) \cdot \frac{1}{2} \]

       3. *-commutative N/A

          \[\leadsto \left(\left({y}^{2} \cdot x\right) \cdot {t}^{2}\right) \cdot \frac{1}{2} \]

       4. associate-*l* N/A

          \[\leadsto \left({y}^{2} \cdot \left(x \cdot {t}^{2}\right)\right) \cdot \frac{1}{2} \]

       5. *-commutative N/A

          \[\leadsto \left({y}^{2} \cdot \left({t}^{2} \cdot x\right)\right) \cdot \frac{1}{2} \]

       6. associate-*r* N/A

          \[\leadsto {y}^{2} \cdot \color{blue}{\left(\left({t}^{2} \cdot x\right) \cdot \frac{1}{2}\right)} \]

       7. *-commutative N/A

          \[\leadsto {y}^{2} \cdot \left(\frac{1}{2} \cdot \color{blue}{\left({t}^{2} \cdot x\right)}\right) \]

       8. unpow2 N/A

          \[\leadsto \left(y \cdot y\right) \cdot \left(\color{blue}{\frac{1}{2}} \cdot \left({t}^{2} \cdot x\right)\right) \]

       9. associate-*l* N/A

          \[\leadsto y \cdot \color{blue}{\left(y \cdot \left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right)} \]

       10. *-commutative N/A

           \[\leadsto y \cdot \left(y \cdot \left(\left({t}^{2} \cdot x\right) \cdot \color{blue}{\frac{1}{2}}\right)\right) \]

       11. associate-*r* N/A

           \[\leadsto y \cdot \left(\left(y \cdot \left({t}^{2} \cdot x\right)\right) \cdot \color{blue}{\frac{1}{2}}\right) \]

       12. *-commutative N/A

           \[\leadsto y \cdot \left(\left(y \cdot \left(x \cdot {t}^{2}\right)\right) \cdot \frac{1}{2}\right) \]

       13. associate-*l* N/A

           \[\leadsto y \cdot \left(\left(\left(y \cdot x\right) \cdot {t}^{2}\right) \cdot \frac{1}{2}\right) \]

       14. *-commutative N/A

           \[\leadsto y \cdot \left(\left(\left(x \cdot y\right) \cdot {t}^{2}\right) \cdot \frac{1}{2}\right) \]

       15. *-commutative N/A

           \[\leadsto y \cdot \left(\left({t}^{2} \cdot \left(x \cdot y\right)\right) \cdot \frac{1}{2}\right) \]

       16. *-commutative N/A

           \[\leadsto y \cdot \left(\frac{1}{2} \cdot \color{blue}{\left({t}^{2} \cdot \left(x \cdot y\right)\right)}\right) \]

       17. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{1}{2} \cdot \left({t}^{2} \cdot \left(x \cdot y\right)\right)\right)}\right) \]

       18. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{\left({t}^{2} \cdot \left(x \cdot y\right)\right)}\right)\right) \]

       19. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(\frac{1}{2}, \left(\left(x \cdot y\right) \cdot \color{blue}{{t}^{2}}\right)\right)\right) \]

       20. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(\frac{1}{2}, \left(\left(y \cdot x\right) \cdot {\color{blue}{t}}^{2}\right)\right)\right) \]

       21. associate-*l* N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(\frac{1}{2}, \left(y \cdot \color{blue}{\left(x \cdot {t}^{2}\right)}\right)\right)\right) \]

   13. Simplified 52.7%

       \[\leadsto \color{blue}{y \cdot \left(0.5 \cdot \left(y \cdot \left(x \cdot \left(t \cdot t\right)\right)\right)\right)} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 20: 45.9% accurate, 12.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{-59}:\\ \;\;\;\;\frac{x \cdot 2}{b \cdot \left(b \cdot \left(a \cdot a\right)\right)}\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-133}:\\ \;\;\;\;x - b \cdot \left(x \cdot a\right)\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-31}:\\ \;\;\;\;\left(y \cdot y\right) \cdot \frac{x}{y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(0.5 \cdot \left(y \cdot \left(x \cdot \left(t \cdot t\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.35e-59)
   (/ (* x 2.0) (* b (* b (* a a))))
   (if (<= y 1.65e-133)
     (- x (* b (* x a)))
     (if (<= y 1.5e-31)
       (* (* y y) (/ x (* y y)))
       (* y (* 0.5 (* y (* x (* t t)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.35e-59) {
		tmp = (x * 2.0) / (b * (b * (a * a)));
	} else if (y <= 1.65e-133) {
		tmp = x - (b * (x * a));
	} else if (y <= 1.5e-31) {
		tmp = (y * y) * (x / (y * y));
	} else {
		tmp = y * (0.5 * (y * (x * (t * t))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-1.35d-59)) then
        tmp = (x * 2.0d0) / (b * (b * (a * a)))
    else if (y <= 1.65d-133) then
        tmp = x - (b * (x * a))
    else if (y <= 1.5d-31) then
        tmp = (y * y) * (x / (y * y))
    else
        tmp = y * (0.5d0 * (y * (x * (t * t))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.35e-59) {
		tmp = (x * 2.0) / (b * (b * (a * a)));
	} else if (y <= 1.65e-133) {
		tmp = x - (b * (x * a));
	} else if (y <= 1.5e-31) {
		tmp = (y * y) * (x / (y * y));
	} else {
		tmp = y * (0.5 * (y * (x * (t * t))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.35e-59:
		tmp = (x * 2.0) / (b * (b * (a * a)))
	elif y <= 1.65e-133:
		tmp = x - (b * (x * a))
	elif y <= 1.5e-31:
		tmp = (y * y) * (x / (y * y))
	else:
		tmp = y * (0.5 * (y * (x * (t * t))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.35e-59)
		tmp = Float64(Float64(x * 2.0) / Float64(b * Float64(b * Float64(a * a))));
	elseif (y <= 1.65e-133)
		tmp = Float64(x - Float64(b * Float64(x * a)));
	elseif (y <= 1.5e-31)
		tmp = Float64(Float64(y * y) * Float64(x / Float64(y * y)));
	else
		tmp = Float64(y * Float64(0.5 * Float64(y * Float64(x * Float64(t * t)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1.35e-59)
		tmp = (x * 2.0) / (b * (b * (a * a)));
	elseif (y <= 1.65e-133)
		tmp = x - (b * (x * a));
	elseif (y <= 1.5e-31)
		tmp = (y * y) * (x / (y * y));
	else
		tmp = y * (0.5 * (y * (x * (t * t))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.35e-59], N[(N[(x * 2.0), $MachinePrecision] / N[(b * N[(b * N[(a * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.65e-133], N[(x - N[(b * N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.5e-31], N[(N[(y * y), $MachinePrecision] * N[(x / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(0.5 * N[(y * N[(x * N[(t * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.3499999999999999e-59

   1. Initial program 98.7%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 98.7%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(a \cdot b\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 36.3%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, b\right)\right)\right) \]

   7. Simplified 36.3%

      \[\leadsto \frac{x}{e^{\color{blue}{a \cdot b}}} \]

   8. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + b \cdot \left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)\right)}\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(b \cdot \left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \color{blue}{\left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \color{blue}{\left(\frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right)\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(\left(\frac{1}{2} \cdot {a}^{2}\right) \cdot \color{blue}{b}\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\left(\frac{1}{2} \cdot {a}^{2}\right), \color{blue}{b}\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left({a}^{2}\right)\right), b\right)\right)\right)\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left(a \cdot a\right)\right), b\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 22.2%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(a, a\right)\right), b\right)\right)\right)\right)\right) \]

   10. Simplified 22.2%

       \[\leadsto \frac{x}{\color{blue}{1 + b \cdot \left(a + \left(0.5 \cdot \left(a \cdot a\right)\right) \cdot b\right)}} \]

   11. Taylor expanded in b around inf

       \[\leadsto \color{blue}{2 \cdot \frac{x}{{a}^{2} \cdot {b}^{2}}} \]
   12. Step-by-step derivation

       1. associate-*r/ N/A

          \[\leadsto \frac{2 \cdot x}{\color{blue}{{a}^{2} \cdot {b}^{2}}} \]

       2. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left(2 \cdot x\right), \color{blue}{\left({a}^{2} \cdot {b}^{2}\right)}\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(2, x\right), \left(\color{blue}{{a}^{2}} \cdot {b}^{2}\right)\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(2, x\right), \left({b}^{2} \cdot \color{blue}{{a}^{2}}\right)\right) \]

       5. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(2, x\right), \left(\left(b \cdot b\right) \cdot {\color{blue}{a}}^{2}\right)\right) \]

       6. associate-*l* N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(2, x\right), \left(b \cdot \color{blue}{\left(b \cdot {a}^{2}\right)}\right)\right) \]

       7. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(2, x\right), \left(b \cdot \left({a}^{2} \cdot \color{blue}{b}\right)\right)\right) \]

       8. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(2, x\right), \mathsf{*.f64}\left(b, \color{blue}{\left({a}^{2} \cdot b\right)}\right)\right) \]

       9. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(2, x\right), \mathsf{*.f64}\left(b, \left(b \cdot \color{blue}{{a}^{2}}\right)\right)\right) \]

       10. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(2, x\right), \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(b, \color{blue}{\left({a}^{2}\right)}\right)\right)\right) \]

       11. unpow2 N/A

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(2, x\right), \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(b, \left(a \cdot \color{blue}{a}\right)\right)\right)\right) \]

       12. *-lowering-*.f64 39.1%

           \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(2, x\right), \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \color{blue}{a}\right)\right)\right)\right) \]

   13. Simplified 39.1%

       \[\leadsto \color{blue}{\frac{2 \cdot x}{b \cdot \left(b \cdot \left(a \cdot a\right)\right)}} \]

   if -1.3499999999999999e-59 < y < 1.65000000000000005e-133

   1. Initial program 93.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 93.0%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(a \cdot b\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 83.3%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, b\right)\right)\right) \]

   7. Simplified 83.3%

      \[\leadsto \frac{x}{e^{\color{blue}{a \cdot b}}} \]

   8. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + b \cdot \left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)\right)}\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(b \cdot \left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \color{blue}{\left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \color{blue}{\left(\frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right)\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(\left(\frac{1}{2} \cdot {a}^{2}\right) \cdot \color{blue}{b}\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\left(\frac{1}{2} \cdot {a}^{2}\right), \color{blue}{b}\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left({a}^{2}\right)\right), b\right)\right)\right)\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left(a \cdot a\right)\right), b\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 56.2%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(a, a\right)\right), b\right)\right)\right)\right)\right) \]

   10. Simplified 56.2%

       \[\leadsto \frac{x}{\color{blue}{1 + b \cdot \left(a + \left(0.5 \cdot \left(a \cdot a\right)\right) \cdot b\right)}} \]

   11. Taylor expanded in b around 0

       \[\leadsto \color{blue}{x + -1 \cdot \left(a \cdot \left(b \cdot x\right)\right)} \]
   12. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto x + \left(\mathsf{neg}\left(a \cdot \left(b \cdot x\right)\right)\right) \]

       2. unsub-neg N/A

          \[\leadsto x - \color{blue}{a \cdot \left(b \cdot x\right)} \]

       3. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(a \cdot \left(b \cdot x\right)\right)}\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(a, \color{blue}{\left(b \cdot x\right)}\right)\right) \]

       5. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(a, \left(x \cdot \color{blue}{b}\right)\right)\right) \]

       6. *-lowering-*.f64 44.9%

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(x, \color{blue}{b}\right)\right)\right) \]

   13. Simplified 44.9%

       \[\leadsto \color{blue}{x - a \cdot \left(x \cdot b\right)} \]
   14. Step-by-step derivation

       1. associate-*r* N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \left(\left(a \cdot x\right) \cdot \color{blue}{b}\right)\right) \]

       2. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\left(a \cdot x\right), \color{blue}{b}\right)\right) \]

       3. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\left(x \cdot a\right), b\right)\right) \]

       4. *-lowering-*.f64 49.7%

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, a\right), b\right)\right) \]

   15. Applied egg-rr 49.7%

       \[\leadsto x - \color{blue}{\left(x \cdot a\right) \cdot b} \]

   if 1.65000000000000005e-133 < y < 1.49999999999999991e-31

   1. Initial program 100.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(t \cdot y\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\left(y \cdot t\right)\right)\right) \]

      2. *-lowering-*.f64 71.8%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, t\right)\right)\right) \]

   7. Simplified 71.8%

      \[\leadsto \frac{x}{e^{\color{blue}{y \cdot t}}} \]

   8. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x + y \cdot \left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) - t \cdot x\right)} \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot \left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) - t \cdot x\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) - t \cdot x\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right)\right), \color{blue}{\left(t \cdot x\right)}\right)\right)\right) \]

   10. Simplified 58.3%

       \[\leadsto \color{blue}{x + y \cdot \left(y \cdot \left(0.5 \cdot \left(x \cdot \left(t \cdot t\right)\right)\right) - x \cdot t\right)} \]

   11. Taylor expanded in y around -inf

       \[\leadsto \color{blue}{{y}^{2} \cdot \left(-1 \cdot \frac{-1 \cdot \frac{x}{y} + t \cdot x}{y} + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)} \]
   12. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left({y}^{2}\right), \color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{x}{y} + t \cdot x}{y} + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)}\right) \]

       2. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(y \cdot y\right), \left(\color{blue}{-1 \cdot \frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}} + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \left(\color{blue}{-1 \cdot \frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}} + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) \]

       4. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right) + \color{blue}{-1 \cdot \frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}}\right)\right) \]

       5. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right) + \left(\mathsf{neg}\left(\frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}\right)\right)\right)\right) \]

       6. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right) - \color{blue}{\frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}}\right)\right) \]

       7. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right), \color{blue}{\left(\frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}\right)}\right)\right) \]

       8. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\left(\left({t}^{2} \cdot x\right) \cdot \frac{1}{2}\right), \left(\frac{\color{blue}{-1 \cdot \frac{x}{y} + t \cdot x}}{y}\right)\right)\right) \]

       9. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\left(\left(x \cdot {t}^{2}\right) \cdot \frac{1}{2}\right), \left(\frac{\color{blue}{-1 \cdot \frac{x}{y}} + t \cdot x}{y}\right)\right)\right) \]

       10. associate-*l* N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\left(x \cdot \left({t}^{2} \cdot \frac{1}{2}\right)\right), \left(\frac{\color{blue}{-1 \cdot \frac{x}{y} + t \cdot x}}{y}\right)\right)\right) \]

       11. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \left({t}^{2} \cdot \frac{1}{2}\right)\right), \left(\frac{\color{blue}{-1 \cdot \frac{x}{y} + t \cdot x}}{y}\right)\right)\right) \]

       12. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\left({t}^{2}\right), \frac{1}{2}\right)\right), \left(\frac{-1 \cdot \frac{x}{y} + \color{blue}{t \cdot x}}{y}\right)\right)\right) \]

       13. unpow2 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\left(t \cdot t\right), \frac{1}{2}\right)\right), \left(\frac{-1 \cdot \frac{x}{y} + \color{blue}{t} \cdot x}{y}\right)\right)\right) \]

       14. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, t\right), \frac{1}{2}\right)\right), \left(\frac{-1 \cdot \frac{x}{y} + \color{blue}{t} \cdot x}{y}\right)\right)\right) \]

       15. /-lowering-/.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, t\right), \frac{1}{2}\right)\right), \mathsf{/.f64}\left(\left(-1 \cdot \frac{x}{y} + t \cdot x\right), \color{blue}{y}\right)\right)\right) \]

   13. Simplified 66.6%

       \[\leadsto \color{blue}{\left(y \cdot y\right) \cdot \left(x \cdot \left(\left(t \cdot t\right) \cdot 0.5\right) - \frac{x \cdot t - \frac{x}{y}}{y}\right)} \]

   14. Taylor expanded in t around 0

       \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \color{blue}{\left(\frac{x}{{y}^{2}}\right)}\right) \]
   15. Step-by-step derivation

       1. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{/.f64}\left(x, \color{blue}{\left({y}^{2}\right)}\right)\right) \]

       2. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{/.f64}\left(x, \left(y \cdot \color{blue}{y}\right)\right)\right) \]

       3. *-lowering-*.f64 62.6%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{y}\right)\right)\right) \]

   16. Simplified 62.6%

       \[\leadsto \left(y \cdot y\right) \cdot \color{blue}{\frac{x}{y \cdot y}} \]

   if 1.49999999999999991e-31 < y

   1. Initial program 96.7%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 96.8%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(t \cdot y\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\left(y \cdot t\right)\right)\right) \]

      2. *-lowering-*.f64 57.0%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, t\right)\right)\right) \]

   7. Simplified 57.0%

      \[\leadsto \frac{x}{e^{\color{blue}{y \cdot t}}} \]

   8. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x + y \cdot \left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) - t \cdot x\right)} \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot \left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) - t \cdot x\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) - t \cdot x\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right)\right), \color{blue}{\left(t \cdot x\right)}\right)\right)\right) \]

   10. Simplified 28.3%

       \[\leadsto \color{blue}{x + y \cdot \left(y \cdot \left(0.5 \cdot \left(x \cdot \left(t \cdot t\right)\right)\right) - x \cdot t\right)} \]

   11. Taylor expanded in y around inf

       \[\leadsto \color{blue}{\frac{1}{2} \cdot \left({t}^{2} \cdot \left(x \cdot {y}^{2}\right)\right)} \]
   12. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \left({t}^{2} \cdot \left(x \cdot {y}^{2}\right)\right) \cdot \color{blue}{\frac{1}{2}} \]

       2. *-commutative N/A

          \[\leadsto \left(\left(x \cdot {y}^{2}\right) \cdot {t}^{2}\right) \cdot \frac{1}{2} \]

       3. *-commutative N/A

          \[\leadsto \left(\left({y}^{2} \cdot x\right) \cdot {t}^{2}\right) \cdot \frac{1}{2} \]

       4. associate-*l* N/A

          \[\leadsto \left({y}^{2} \cdot \left(x \cdot {t}^{2}\right)\right) \cdot \frac{1}{2} \]

       5. *-commutative N/A

          \[\leadsto \left({y}^{2} \cdot \left({t}^{2} \cdot x\right)\right) \cdot \frac{1}{2} \]

       6. associate-*r* N/A

          \[\leadsto {y}^{2} \cdot \color{blue}{\left(\left({t}^{2} \cdot x\right) \cdot \frac{1}{2}\right)} \]

       7. *-commutative N/A

          \[\leadsto {y}^{2} \cdot \left(\frac{1}{2} \cdot \color{blue}{\left({t}^{2} \cdot x\right)}\right) \]

       8. unpow2 N/A

          \[\leadsto \left(y \cdot y\right) \cdot \left(\color{blue}{\frac{1}{2}} \cdot \left({t}^{2} \cdot x\right)\right) \]

       9. associate-*l* N/A

          \[\leadsto y \cdot \color{blue}{\left(y \cdot \left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right)} \]

       10. *-commutative N/A

           \[\leadsto y \cdot \left(y \cdot \left(\left({t}^{2} \cdot x\right) \cdot \color{blue}{\frac{1}{2}}\right)\right) \]

       11. associate-*r* N/A

           \[\leadsto y \cdot \left(\left(y \cdot \left({t}^{2} \cdot x\right)\right) \cdot \color{blue}{\frac{1}{2}}\right) \]

       12. *-commutative N/A

           \[\leadsto y \cdot \left(\left(y \cdot \left(x \cdot {t}^{2}\right)\right) \cdot \frac{1}{2}\right) \]

       13. associate-*l* N/A

           \[\leadsto y \cdot \left(\left(\left(y \cdot x\right) \cdot {t}^{2}\right) \cdot \frac{1}{2}\right) \]

       14. *-commutative N/A

           \[\leadsto y \cdot \left(\left(\left(x \cdot y\right) \cdot {t}^{2}\right) \cdot \frac{1}{2}\right) \]

       15. *-commutative N/A

           \[\leadsto y \cdot \left(\left({t}^{2} \cdot \left(x \cdot y\right)\right) \cdot \frac{1}{2}\right) \]

       16. *-commutative N/A

           \[\leadsto y \cdot \left(\frac{1}{2} \cdot \color{blue}{\left({t}^{2} \cdot \left(x \cdot y\right)\right)}\right) \]

       17. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{1}{2} \cdot \left({t}^{2} \cdot \left(x \cdot y\right)\right)\right)}\right) \]

       18. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{\left({t}^{2} \cdot \left(x \cdot y\right)\right)}\right)\right) \]

       19. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(\frac{1}{2}, \left(\left(x \cdot y\right) \cdot \color{blue}{{t}^{2}}\right)\right)\right) \]

       20. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(\frac{1}{2}, \left(\left(y \cdot x\right) \cdot {\color{blue}{t}}^{2}\right)\right)\right) \]

       21. associate-*l* N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(\frac{1}{2}, \left(y \cdot \color{blue}{\left(x \cdot {t}^{2}\right)}\right)\right)\right) \]

   13. Simplified 51.8%

       \[\leadsto \color{blue}{y \cdot \left(0.5 \cdot \left(y \cdot \left(x \cdot \left(t \cdot t\right)\right)\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 48.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{-59}:\\ \;\;\;\;\frac{x \cdot 2}{b \cdot \left(b \cdot \left(a \cdot a\right)\right)}\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-133}:\\ \;\;\;\;x - b \cdot \left(x \cdot a\right)\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-31}:\\ \;\;\;\;\left(y \cdot y\right) \cdot \frac{x}{y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(0.5 \cdot \left(y \cdot \left(x \cdot \left(t \cdot t\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 45.7% accurate, 12.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{-60}:\\ \;\;\;\;\frac{x}{0.5 \cdot \left(a \cdot \left(a \cdot \left(b \cdot b\right)\right)\right)}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-133}:\\ \;\;\;\;x - b \cdot \left(x \cdot a\right)\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-34}:\\ \;\;\;\;\left(y \cdot y\right) \cdot \frac{x}{y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(0.5 \cdot \left(y \cdot \left(x \cdot \left(t \cdot t\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -8.5e-60)
   (/ x (* 0.5 (* a (* a (* b b)))))
   (if (<= y 1.9e-133)
     (- x (* b (* x a)))
     (if (<= y 3.4e-34)
       (* (* y y) (/ x (* y y)))
       (* y (* 0.5 (* y (* x (* t t)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -8.5e-60) {
		tmp = x / (0.5 * (a * (a * (b * b))));
	} else if (y <= 1.9e-133) {
		tmp = x - (b * (x * a));
	} else if (y <= 3.4e-34) {
		tmp = (y * y) * (x / (y * y));
	} else {
		tmp = y * (0.5 * (y * (x * (t * t))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-8.5d-60)) then
        tmp = x / (0.5d0 * (a * (a * (b * b))))
    else if (y <= 1.9d-133) then
        tmp = x - (b * (x * a))
    else if (y <= 3.4d-34) then
        tmp = (y * y) * (x / (y * y))
    else
        tmp = y * (0.5d0 * (y * (x * (t * t))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -8.5e-60) {
		tmp = x / (0.5 * (a * (a * (b * b))));
	} else if (y <= 1.9e-133) {
		tmp = x - (b * (x * a));
	} else if (y <= 3.4e-34) {
		tmp = (y * y) * (x / (y * y));
	} else {
		tmp = y * (0.5 * (y * (x * (t * t))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -8.5e-60:
		tmp = x / (0.5 * (a * (a * (b * b))))
	elif y <= 1.9e-133:
		tmp = x - (b * (x * a))
	elif y <= 3.4e-34:
		tmp = (y * y) * (x / (y * y))
	else:
		tmp = y * (0.5 * (y * (x * (t * t))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -8.5e-60)
		tmp = Float64(x / Float64(0.5 * Float64(a * Float64(a * Float64(b * b)))));
	elseif (y <= 1.9e-133)
		tmp = Float64(x - Float64(b * Float64(x * a)));
	elseif (y <= 3.4e-34)
		tmp = Float64(Float64(y * y) * Float64(x / Float64(y * y)));
	else
		tmp = Float64(y * Float64(0.5 * Float64(y * Float64(x * Float64(t * t)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -8.5e-60)
		tmp = x / (0.5 * (a * (a * (b * b))));
	elseif (y <= 1.9e-133)
		tmp = x - (b * (x * a));
	elseif (y <= 3.4e-34)
		tmp = (y * y) * (x / (y * y));
	else
		tmp = y * (0.5 * (y * (x * (t * t))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -8.5e-60], N[(x / N[(0.5 * N[(a * N[(a * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.9e-133], N[(x - N[(b * N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.4e-34], N[(N[(y * y), $MachinePrecision] * N[(x / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(0.5 * N[(y * N[(x * N[(t * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -8.50000000000000044e-60

   1. Initial program 98.7%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 98.7%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(a \cdot b\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 36.3%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, b\right)\right)\right) \]

   7. Simplified 36.3%

      \[\leadsto \frac{x}{e^{\color{blue}{a \cdot b}}} \]

   8. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + b \cdot \left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)\right)}\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(b \cdot \left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \color{blue}{\left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \color{blue}{\left(\frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right)\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(\left(\frac{1}{2} \cdot {a}^{2}\right) \cdot \color{blue}{b}\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\left(\frac{1}{2} \cdot {a}^{2}\right), \color{blue}{b}\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left({a}^{2}\right)\right), b\right)\right)\right)\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left(a \cdot a\right)\right), b\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 22.2%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(a, a\right)\right), b\right)\right)\right)\right)\right) \]

   10. Simplified 22.2%

       \[\leadsto \frac{x}{\color{blue}{1 + b \cdot \left(a + \left(0.5 \cdot \left(a \cdot a\right)\right) \cdot b\right)}} \]
   11. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(b \cdot \color{blue}{\left(\frac{1}{2} \cdot \left(a \cdot a\right)\right)}\right)\right)\right)\right)\right) \]

       2. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(b \cdot \left(\left(\frac{1}{2} \cdot a\right) \cdot \color{blue}{a}\right)\right)\right)\right)\right)\right) \]

       3. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(\left(b \cdot \left(\frac{1}{2} \cdot a\right)\right) \cdot \color{blue}{a}\right)\right)\right)\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\left(b \cdot \left(\frac{1}{2} \cdot a\right)\right), \color{blue}{a}\right)\right)\right)\right)\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \left(\frac{1}{2} \cdot a\right)\right), a\right)\right)\right)\right)\right) \]

       6. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \left(a \cdot \frac{1}{2}\right)\right), a\right)\right)\right)\right)\right) \]

       7. *-lowering-*.f64 20.9%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \frac{1}{2}\right)\right), a\right)\right)\right)\right)\right) \]

   12. Applied egg-rr 20.9%

       \[\leadsto \frac{x}{1 + b \cdot \left(a + \color{blue}{\left(b \cdot \left(a \cdot 0.5\right)\right) \cdot a}\right)} \]

   13. Taylor expanded in b around inf

       \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(\frac{1}{2} \cdot \left({a}^{2} \cdot {b}^{2}\right)\right)}\right) \]
   14. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{\left({a}^{2} \cdot {b}^{2}\right)}\right)\right) \]

       2. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{2}, \left(\left(a \cdot a\right) \cdot {\color{blue}{b}}^{2}\right)\right)\right) \]

       3. associate-*l* N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{2}, \left(a \cdot \color{blue}{\left(a \cdot {b}^{2}\right)}\right)\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(a, \color{blue}{\left(a \cdot {b}^{2}\right)}\right)\right)\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(a, \color{blue}{\left({b}^{2}\right)}\right)\right)\right)\right) \]

       6. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(a, \left(b \cdot \color{blue}{b}\right)\right)\right)\right)\right) \]

       7. *-lowering-*.f64 37.9%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(b, \color{blue}{b}\right)\right)\right)\right)\right) \]

   15. Simplified 37.9%

       \[\leadsto \frac{x}{\color{blue}{0.5 \cdot \left(a \cdot \left(a \cdot \left(b \cdot b\right)\right)\right)}} \]

   if -8.50000000000000044e-60 < y < 1.9000000000000002e-133

   1. Initial program 93.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 93.0%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(a \cdot b\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 83.3%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, b\right)\right)\right) \]

   7. Simplified 83.3%

      \[\leadsto \frac{x}{e^{\color{blue}{a \cdot b}}} \]

   8. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + b \cdot \left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)\right)}\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(b \cdot \left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \color{blue}{\left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \color{blue}{\left(\frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right)\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(\left(\frac{1}{2} \cdot {a}^{2}\right) \cdot \color{blue}{b}\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\left(\frac{1}{2} \cdot {a}^{2}\right), \color{blue}{b}\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left({a}^{2}\right)\right), b\right)\right)\right)\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left(a \cdot a\right)\right), b\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 56.2%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(a, a\right)\right), b\right)\right)\right)\right)\right) \]

   10. Simplified 56.2%

       \[\leadsto \frac{x}{\color{blue}{1 + b \cdot \left(a + \left(0.5 \cdot \left(a \cdot a\right)\right) \cdot b\right)}} \]

   11. Taylor expanded in b around 0

       \[\leadsto \color{blue}{x + -1 \cdot \left(a \cdot \left(b \cdot x\right)\right)} \]
   12. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto x + \left(\mathsf{neg}\left(a \cdot \left(b \cdot x\right)\right)\right) \]

       2. unsub-neg N/A

          \[\leadsto x - \color{blue}{a \cdot \left(b \cdot x\right)} \]

       3. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(a \cdot \left(b \cdot x\right)\right)}\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(a, \color{blue}{\left(b \cdot x\right)}\right)\right) \]

       5. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(a, \left(x \cdot \color{blue}{b}\right)\right)\right) \]

       6. *-lowering-*.f64 44.9%

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(x, \color{blue}{b}\right)\right)\right) \]

   13. Simplified 44.9%

       \[\leadsto \color{blue}{x - a \cdot \left(x \cdot b\right)} \]
   14. Step-by-step derivation

       1. associate-*r* N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \left(\left(a \cdot x\right) \cdot \color{blue}{b}\right)\right) \]

       2. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\left(a \cdot x\right), \color{blue}{b}\right)\right) \]

       3. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\left(x \cdot a\right), b\right)\right) \]

       4. *-lowering-*.f64 49.7%

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, a\right), b\right)\right) \]

   15. Applied egg-rr 49.7%

       \[\leadsto x - \color{blue}{\left(x \cdot a\right) \cdot b} \]

   if 1.9000000000000002e-133 < y < 3.4000000000000001e-34

   1. Initial program 100.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(t \cdot y\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\left(y \cdot t\right)\right)\right) \]

      2. *-lowering-*.f64 71.8%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, t\right)\right)\right) \]

   7. Simplified 71.8%

      \[\leadsto \frac{x}{e^{\color{blue}{y \cdot t}}} \]

   8. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x + y \cdot \left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) - t \cdot x\right)} \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot \left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) - t \cdot x\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) - t \cdot x\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right)\right), \color{blue}{\left(t \cdot x\right)}\right)\right)\right) \]

   10. Simplified 58.3%

       \[\leadsto \color{blue}{x + y \cdot \left(y \cdot \left(0.5 \cdot \left(x \cdot \left(t \cdot t\right)\right)\right) - x \cdot t\right)} \]

   11. Taylor expanded in y around -inf

       \[\leadsto \color{blue}{{y}^{2} \cdot \left(-1 \cdot \frac{-1 \cdot \frac{x}{y} + t \cdot x}{y} + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)} \]
   12. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left({y}^{2}\right), \color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{x}{y} + t \cdot x}{y} + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)}\right) \]

       2. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(y \cdot y\right), \left(\color{blue}{-1 \cdot \frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}} + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \left(\color{blue}{-1 \cdot \frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}} + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) \]

       4. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right) + \color{blue}{-1 \cdot \frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}}\right)\right) \]

       5. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right) + \left(\mathsf{neg}\left(\frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}\right)\right)\right)\right) \]

       6. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right) - \color{blue}{\frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}}\right)\right) \]

       7. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right), \color{blue}{\left(\frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}\right)}\right)\right) \]

       8. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\left(\left({t}^{2} \cdot x\right) \cdot \frac{1}{2}\right), \left(\frac{\color{blue}{-1 \cdot \frac{x}{y} + t \cdot x}}{y}\right)\right)\right) \]

       9. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\left(\left(x \cdot {t}^{2}\right) \cdot \frac{1}{2}\right), \left(\frac{\color{blue}{-1 \cdot \frac{x}{y}} + t \cdot x}{y}\right)\right)\right) \]

       10. associate-*l* N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\left(x \cdot \left({t}^{2} \cdot \frac{1}{2}\right)\right), \left(\frac{\color{blue}{-1 \cdot \frac{x}{y} + t \cdot x}}{y}\right)\right)\right) \]

       11. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \left({t}^{2} \cdot \frac{1}{2}\right)\right), \left(\frac{\color{blue}{-1 \cdot \frac{x}{y} + t \cdot x}}{y}\right)\right)\right) \]

       12. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\left({t}^{2}\right), \frac{1}{2}\right)\right), \left(\frac{-1 \cdot \frac{x}{y} + \color{blue}{t \cdot x}}{y}\right)\right)\right) \]

       13. unpow2 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\left(t \cdot t\right), \frac{1}{2}\right)\right), \left(\frac{-1 \cdot \frac{x}{y} + \color{blue}{t} \cdot x}{y}\right)\right)\right) \]

       14. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, t\right), \frac{1}{2}\right)\right), \left(\frac{-1 \cdot \frac{x}{y} + \color{blue}{t} \cdot x}{y}\right)\right)\right) \]

       15. /-lowering-/.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, t\right), \frac{1}{2}\right)\right), \mathsf{/.f64}\left(\left(-1 \cdot \frac{x}{y} + t \cdot x\right), \color{blue}{y}\right)\right)\right) \]

   13. Simplified 66.6%

       \[\leadsto \color{blue}{\left(y \cdot y\right) \cdot \left(x \cdot \left(\left(t \cdot t\right) \cdot 0.5\right) - \frac{x \cdot t - \frac{x}{y}}{y}\right)} \]

   14. Taylor expanded in t around 0

       \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \color{blue}{\left(\frac{x}{{y}^{2}}\right)}\right) \]
   15. Step-by-step derivation

       1. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{/.f64}\left(x, \color{blue}{\left({y}^{2}\right)}\right)\right) \]

       2. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{/.f64}\left(x, \left(y \cdot \color{blue}{y}\right)\right)\right) \]

       3. *-lowering-*.f64 62.6%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{y}\right)\right)\right) \]

   16. Simplified 62.6%

       \[\leadsto \left(y \cdot y\right) \cdot \color{blue}{\frac{x}{y \cdot y}} \]

   if 3.4000000000000001e-34 < y

   1. Initial program 96.7%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 96.8%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(t \cdot y\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\left(y \cdot t\right)\right)\right) \]

      2. *-lowering-*.f64 57.0%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, t\right)\right)\right) \]

   7. Simplified 57.0%

      \[\leadsto \frac{x}{e^{\color{blue}{y \cdot t}}} \]

   8. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x + y \cdot \left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) - t \cdot x\right)} \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot \left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) - t \cdot x\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) - t \cdot x\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right)\right), \color{blue}{\left(t \cdot x\right)}\right)\right)\right) \]

   10. Simplified 28.3%

       \[\leadsto \color{blue}{x + y \cdot \left(y \cdot \left(0.5 \cdot \left(x \cdot \left(t \cdot t\right)\right)\right) - x \cdot t\right)} \]

   11. Taylor expanded in y around inf

       \[\leadsto \color{blue}{\frac{1}{2} \cdot \left({t}^{2} \cdot \left(x \cdot {y}^{2}\right)\right)} \]
   12. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \left({t}^{2} \cdot \left(x \cdot {y}^{2}\right)\right) \cdot \color{blue}{\frac{1}{2}} \]

       2. *-commutative N/A

          \[\leadsto \left(\left(x \cdot {y}^{2}\right) \cdot {t}^{2}\right) \cdot \frac{1}{2} \]

       3. *-commutative N/A

          \[\leadsto \left(\left({y}^{2} \cdot x\right) \cdot {t}^{2}\right) \cdot \frac{1}{2} \]

       4. associate-*l* N/A

          \[\leadsto \left({y}^{2} \cdot \left(x \cdot {t}^{2}\right)\right) \cdot \frac{1}{2} \]

       5. *-commutative N/A

          \[\leadsto \left({y}^{2} \cdot \left({t}^{2} \cdot x\right)\right) \cdot \frac{1}{2} \]

       6. associate-*r* N/A

          \[\leadsto {y}^{2} \cdot \color{blue}{\left(\left({t}^{2} \cdot x\right) \cdot \frac{1}{2}\right)} \]

       7. *-commutative N/A

          \[\leadsto {y}^{2} \cdot \left(\frac{1}{2} \cdot \color{blue}{\left({t}^{2} \cdot x\right)}\right) \]

       8. unpow2 N/A

          \[\leadsto \left(y \cdot y\right) \cdot \left(\color{blue}{\frac{1}{2}} \cdot \left({t}^{2} \cdot x\right)\right) \]

       9. associate-*l* N/A

          \[\leadsto y \cdot \color{blue}{\left(y \cdot \left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right)} \]

       10. *-commutative N/A

           \[\leadsto y \cdot \left(y \cdot \left(\left({t}^{2} \cdot x\right) \cdot \color{blue}{\frac{1}{2}}\right)\right) \]

       11. associate-*r* N/A

           \[\leadsto y \cdot \left(\left(y \cdot \left({t}^{2} \cdot x\right)\right) \cdot \color{blue}{\frac{1}{2}}\right) \]

       12. *-commutative N/A

           \[\leadsto y \cdot \left(\left(y \cdot \left(x \cdot {t}^{2}\right)\right) \cdot \frac{1}{2}\right) \]

       13. associate-*l* N/A

           \[\leadsto y \cdot \left(\left(\left(y \cdot x\right) \cdot {t}^{2}\right) \cdot \frac{1}{2}\right) \]

       14. *-commutative N/A

           \[\leadsto y \cdot \left(\left(\left(x \cdot y\right) \cdot {t}^{2}\right) \cdot \frac{1}{2}\right) \]

       15. *-commutative N/A

           \[\leadsto y \cdot \left(\left({t}^{2} \cdot \left(x \cdot y\right)\right) \cdot \frac{1}{2}\right) \]

       16. *-commutative N/A

           \[\leadsto y \cdot \left(\frac{1}{2} \cdot \color{blue}{\left({t}^{2} \cdot \left(x \cdot y\right)\right)}\right) \]

       17. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{1}{2} \cdot \left({t}^{2} \cdot \left(x \cdot y\right)\right)\right)}\right) \]

       18. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{\left({t}^{2} \cdot \left(x \cdot y\right)\right)}\right)\right) \]

       19. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(\frac{1}{2}, \left(\left(x \cdot y\right) \cdot \color{blue}{{t}^{2}}\right)\right)\right) \]

       20. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(\frac{1}{2}, \left(\left(y \cdot x\right) \cdot {\color{blue}{t}}^{2}\right)\right)\right) \]

       21. associate-*l* N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(\frac{1}{2}, \left(y \cdot \color{blue}{\left(x \cdot {t}^{2}\right)}\right)\right)\right) \]

   13. Simplified 51.8%

       \[\leadsto \color{blue}{y \cdot \left(0.5 \cdot \left(y \cdot \left(x \cdot \left(t \cdot t\right)\right)\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 47.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{-60}:\\ \;\;\;\;\frac{x}{0.5 \cdot \left(a \cdot \left(a \cdot \left(b \cdot b\right)\right)\right)}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-133}:\\ \;\;\;\;x - b \cdot \left(x \cdot a\right)\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-34}:\\ \;\;\;\;\left(y \cdot y\right) \cdot \frac{x}{y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(0.5 \cdot \left(y \cdot \left(x \cdot \left(t \cdot t\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 38.6% accurate, 12.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{+90}:\\ \;\;\;\;\frac{x}{y \cdot t + 1}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-133}:\\ \;\;\;\;x - b \cdot \left(x \cdot a\right)\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-32}:\\ \;\;\;\;\left(y \cdot y\right) \cdot \frac{x}{y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(0.5 \cdot \left(y \cdot \left(x \cdot \left(t \cdot t\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.75e+90)
   (/ x (+ (* y t) 1.0))
   (if (<= y 1.9e-133)
     (- x (* b (* x a)))
     (if (<= y 1.3e-32)
       (* (* y y) (/ x (* y y)))
       (* y (* 0.5 (* y (* x (* t t)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.75e+90) {
		tmp = x / ((y * t) + 1.0);
	} else if (y <= 1.9e-133) {
		tmp = x - (b * (x * a));
	} else if (y <= 1.3e-32) {
		tmp = (y * y) * (x / (y * y));
	} else {
		tmp = y * (0.5 * (y * (x * (t * t))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-1.75d+90)) then
        tmp = x / ((y * t) + 1.0d0)
    else if (y <= 1.9d-133) then
        tmp = x - (b * (x * a))
    else if (y <= 1.3d-32) then
        tmp = (y * y) * (x / (y * y))
    else
        tmp = y * (0.5d0 * (y * (x * (t * t))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.75e+90) {
		tmp = x / ((y * t) + 1.0);
	} else if (y <= 1.9e-133) {
		tmp = x - (b * (x * a));
	} else if (y <= 1.3e-32) {
		tmp = (y * y) * (x / (y * y));
	} else {
		tmp = y * (0.5 * (y * (x * (t * t))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.75e+90:
		tmp = x / ((y * t) + 1.0)
	elif y <= 1.9e-133:
		tmp = x - (b * (x * a))
	elif y <= 1.3e-32:
		tmp = (y * y) * (x / (y * y))
	else:
		tmp = y * (0.5 * (y * (x * (t * t))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.75e+90)
		tmp = Float64(x / Float64(Float64(y * t) + 1.0));
	elseif (y <= 1.9e-133)
		tmp = Float64(x - Float64(b * Float64(x * a)));
	elseif (y <= 1.3e-32)
		tmp = Float64(Float64(y * y) * Float64(x / Float64(y * y)));
	else
		tmp = Float64(y * Float64(0.5 * Float64(y * Float64(x * Float64(t * t)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1.75e+90)
		tmp = x / ((y * t) + 1.0);
	elseif (y <= 1.9e-133)
		tmp = x - (b * (x * a));
	elseif (y <= 1.3e-32)
		tmp = (y * y) * (x / (y * y));
	else
		tmp = y * (0.5 * (y * (x * (t * t))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.75e+90], N[(x / N[(N[(y * t), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.9e-133], N[(x - N[(b * N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.3e-32], N[(N[(y * y), $MachinePrecision] * N[(x / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(0.5 * N[(y * N[(x * N[(t * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.7499999999999999e90

   1. Initial program 100.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(t \cdot y\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\left(y \cdot t\right)\right)\right) \]

      2. *-lowering-*.f64 72.1%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, t\right)\right)\right) \]

   7. Simplified 72.1%

      \[\leadsto \frac{x}{e^{\color{blue}{y \cdot t}}} \]

   8. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + t \cdot y\right)}\right) \]
   9. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(t \cdot y + \color{blue}{1}\right)\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\left(t \cdot y\right), \color{blue}{1}\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\left(y \cdot t\right), 1\right)\right) \]

      4. *-lowering-*.f64 39.7%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, t\right), 1\right)\right) \]

   10. Simplified 39.7%

       \[\leadsto \frac{x}{\color{blue}{y \cdot t + 1}} \]

   if -1.7499999999999999e90 < y < 1.9000000000000002e-133

   1. Initial program 94.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 94.0%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(a \cdot b\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 74.7%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, b\right)\right)\right) \]

   7. Simplified 74.7%

      \[\leadsto \frac{x}{e^{\color{blue}{a \cdot b}}} \]

   8. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + b \cdot \left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)\right)}\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(b \cdot \left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \color{blue}{\left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \color{blue}{\left(\frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right)\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(\left(\frac{1}{2} \cdot {a}^{2}\right) \cdot \color{blue}{b}\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\left(\frac{1}{2} \cdot {a}^{2}\right), \color{blue}{b}\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left({a}^{2}\right)\right), b\right)\right)\right)\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left(a \cdot a\right)\right), b\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 48.5%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(a, a\right)\right), b\right)\right)\right)\right)\right) \]

   10. Simplified 48.5%

       \[\leadsto \frac{x}{\color{blue}{1 + b \cdot \left(a + \left(0.5 \cdot \left(a \cdot a\right)\right) \cdot b\right)}} \]

   11. Taylor expanded in b around 0

       \[\leadsto \color{blue}{x + -1 \cdot \left(a \cdot \left(b \cdot x\right)\right)} \]
   12. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto x + \left(\mathsf{neg}\left(a \cdot \left(b \cdot x\right)\right)\right) \]

       2. unsub-neg N/A

          \[\leadsto x - \color{blue}{a \cdot \left(b \cdot x\right)} \]

       3. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(a \cdot \left(b \cdot x\right)\right)}\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(a, \color{blue}{\left(b \cdot x\right)}\right)\right) \]

       5. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(a, \left(x \cdot \color{blue}{b}\right)\right)\right) \]

       6. *-lowering-*.f64 37.8%

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(x, \color{blue}{b}\right)\right)\right) \]

   13. Simplified 37.8%

       \[\leadsto \color{blue}{x - a \cdot \left(x \cdot b\right)} \]
   14. Step-by-step derivation

       1. associate-*r* N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \left(\left(a \cdot x\right) \cdot \color{blue}{b}\right)\right) \]

       2. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\left(a \cdot x\right), \color{blue}{b}\right)\right) \]

       3. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\left(x \cdot a\right), b\right)\right) \]

       4. *-lowering-*.f64 40.8%

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, a\right), b\right)\right) \]

   15. Applied egg-rr 40.8%

       \[\leadsto x - \color{blue}{\left(x \cdot a\right) \cdot b} \]

   if 1.9000000000000002e-133 < y < 1.2999999999999999e-32

   1. Initial program 100.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(t \cdot y\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\left(y \cdot t\right)\right)\right) \]

      2. *-lowering-*.f64 71.8%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, t\right)\right)\right) \]

   7. Simplified 71.8%

      \[\leadsto \frac{x}{e^{\color{blue}{y \cdot t}}} \]

   8. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x + y \cdot \left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) - t \cdot x\right)} \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot \left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) - t \cdot x\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) - t \cdot x\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right)\right), \color{blue}{\left(t \cdot x\right)}\right)\right)\right) \]

   10. Simplified 58.3%

       \[\leadsto \color{blue}{x + y \cdot \left(y \cdot \left(0.5 \cdot \left(x \cdot \left(t \cdot t\right)\right)\right) - x \cdot t\right)} \]

   11. Taylor expanded in y around -inf

       \[\leadsto \color{blue}{{y}^{2} \cdot \left(-1 \cdot \frac{-1 \cdot \frac{x}{y} + t \cdot x}{y} + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)} \]
   12. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left({y}^{2}\right), \color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{x}{y} + t \cdot x}{y} + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)}\right) \]

       2. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(y \cdot y\right), \left(\color{blue}{-1 \cdot \frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}} + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \left(\color{blue}{-1 \cdot \frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}} + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) \]

       4. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right) + \color{blue}{-1 \cdot \frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}}\right)\right) \]

       5. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right) + \left(\mathsf{neg}\left(\frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}\right)\right)\right)\right) \]

       6. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right) - \color{blue}{\frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}}\right)\right) \]

       7. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right), \color{blue}{\left(\frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}\right)}\right)\right) \]

       8. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\left(\left({t}^{2} \cdot x\right) \cdot \frac{1}{2}\right), \left(\frac{\color{blue}{-1 \cdot \frac{x}{y} + t \cdot x}}{y}\right)\right)\right) \]

       9. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\left(\left(x \cdot {t}^{2}\right) \cdot \frac{1}{2}\right), \left(\frac{\color{blue}{-1 \cdot \frac{x}{y}} + t \cdot x}{y}\right)\right)\right) \]

       10. associate-*l* N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\left(x \cdot \left({t}^{2} \cdot \frac{1}{2}\right)\right), \left(\frac{\color{blue}{-1 \cdot \frac{x}{y} + t \cdot x}}{y}\right)\right)\right) \]

       11. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \left({t}^{2} \cdot \frac{1}{2}\right)\right), \left(\frac{\color{blue}{-1 \cdot \frac{x}{y} + t \cdot x}}{y}\right)\right)\right) \]

       12. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\left({t}^{2}\right), \frac{1}{2}\right)\right), \left(\frac{-1 \cdot \frac{x}{y} + \color{blue}{t \cdot x}}{y}\right)\right)\right) \]

       13. unpow2 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\left(t \cdot t\right), \frac{1}{2}\right)\right), \left(\frac{-1 \cdot \frac{x}{y} + \color{blue}{t} \cdot x}{y}\right)\right)\right) \]

       14. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, t\right), \frac{1}{2}\right)\right), \left(\frac{-1 \cdot \frac{x}{y} + \color{blue}{t} \cdot x}{y}\right)\right)\right) \]

       15. /-lowering-/.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, t\right), \frac{1}{2}\right)\right), \mathsf{/.f64}\left(\left(-1 \cdot \frac{x}{y} + t \cdot x\right), \color{blue}{y}\right)\right)\right) \]

   13. Simplified 66.6%

       \[\leadsto \color{blue}{\left(y \cdot y\right) \cdot \left(x \cdot \left(\left(t \cdot t\right) \cdot 0.5\right) - \frac{x \cdot t - \frac{x}{y}}{y}\right)} \]

   14. Taylor expanded in t around 0

       \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \color{blue}{\left(\frac{x}{{y}^{2}}\right)}\right) \]
   15. Step-by-step derivation

       1. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{/.f64}\left(x, \color{blue}{\left({y}^{2}\right)}\right)\right) \]

       2. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{/.f64}\left(x, \left(y \cdot \color{blue}{y}\right)\right)\right) \]

       3. *-lowering-*.f64 62.6%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{y}\right)\right)\right) \]

   16. Simplified 62.6%

       \[\leadsto \left(y \cdot y\right) \cdot \color{blue}{\frac{x}{y \cdot y}} \]

   if 1.2999999999999999e-32 < y

   1. Initial program 96.7%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 96.8%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(t \cdot y\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\left(y \cdot t\right)\right)\right) \]

      2. *-lowering-*.f64 57.0%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, t\right)\right)\right) \]

   7. Simplified 57.0%

      \[\leadsto \frac{x}{e^{\color{blue}{y \cdot t}}} \]

   8. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x + y \cdot \left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) - t \cdot x\right)} \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot \left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) - t \cdot x\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) - t \cdot x\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right)\right), \color{blue}{\left(t \cdot x\right)}\right)\right)\right) \]

   10. Simplified 28.3%

       \[\leadsto \color{blue}{x + y \cdot \left(y \cdot \left(0.5 \cdot \left(x \cdot \left(t \cdot t\right)\right)\right) - x \cdot t\right)} \]

   11. Taylor expanded in y around inf

       \[\leadsto \color{blue}{\frac{1}{2} \cdot \left({t}^{2} \cdot \left(x \cdot {y}^{2}\right)\right)} \]
   12. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \left({t}^{2} \cdot \left(x \cdot {y}^{2}\right)\right) \cdot \color{blue}{\frac{1}{2}} \]

       2. *-commutative N/A

          \[\leadsto \left(\left(x \cdot {y}^{2}\right) \cdot {t}^{2}\right) \cdot \frac{1}{2} \]

       3. *-commutative N/A

          \[\leadsto \left(\left({y}^{2} \cdot x\right) \cdot {t}^{2}\right) \cdot \frac{1}{2} \]

       4. associate-*l* N/A

          \[\leadsto \left({y}^{2} \cdot \left(x \cdot {t}^{2}\right)\right) \cdot \frac{1}{2} \]

       5. *-commutative N/A

          \[\leadsto \left({y}^{2} \cdot \left({t}^{2} \cdot x\right)\right) \cdot \frac{1}{2} \]

       6. associate-*r* N/A

          \[\leadsto {y}^{2} \cdot \color{blue}{\left(\left({t}^{2} \cdot x\right) \cdot \frac{1}{2}\right)} \]

       7. *-commutative N/A

          \[\leadsto {y}^{2} \cdot \left(\frac{1}{2} \cdot \color{blue}{\left({t}^{2} \cdot x\right)}\right) \]

       8. unpow2 N/A

          \[\leadsto \left(y \cdot y\right) \cdot \left(\color{blue}{\frac{1}{2}} \cdot \left({t}^{2} \cdot x\right)\right) \]

       9. associate-*l* N/A

          \[\leadsto y \cdot \color{blue}{\left(y \cdot \left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right)} \]

       10. *-commutative N/A

           \[\leadsto y \cdot \left(y \cdot \left(\left({t}^{2} \cdot x\right) \cdot \color{blue}{\frac{1}{2}}\right)\right) \]

       11. associate-*r* N/A

           \[\leadsto y \cdot \left(\left(y \cdot \left({t}^{2} \cdot x\right)\right) \cdot \color{blue}{\frac{1}{2}}\right) \]

       12. *-commutative N/A

           \[\leadsto y \cdot \left(\left(y \cdot \left(x \cdot {t}^{2}\right)\right) \cdot \frac{1}{2}\right) \]

       13. associate-*l* N/A

           \[\leadsto y \cdot \left(\left(\left(y \cdot x\right) \cdot {t}^{2}\right) \cdot \frac{1}{2}\right) \]

       14. *-commutative N/A

           \[\leadsto y \cdot \left(\left(\left(x \cdot y\right) \cdot {t}^{2}\right) \cdot \frac{1}{2}\right) \]

       15. *-commutative N/A

           \[\leadsto y \cdot \left(\left({t}^{2} \cdot \left(x \cdot y\right)\right) \cdot \frac{1}{2}\right) \]

       16. *-commutative N/A

           \[\leadsto y \cdot \left(\frac{1}{2} \cdot \color{blue}{\left({t}^{2} \cdot \left(x \cdot y\right)\right)}\right) \]

       17. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{1}{2} \cdot \left({t}^{2} \cdot \left(x \cdot y\right)\right)\right)}\right) \]

       18. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(\frac{1}{2}, \color{blue}{\left({t}^{2} \cdot \left(x \cdot y\right)\right)}\right)\right) \]

       19. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(\frac{1}{2}, \left(\left(x \cdot y\right) \cdot \color{blue}{{t}^{2}}\right)\right)\right) \]

       20. *-commutative N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(\frac{1}{2}, \left(\left(y \cdot x\right) \cdot {\color{blue}{t}}^{2}\right)\right)\right) \]

       21. associate-*l* N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(\frac{1}{2}, \left(y \cdot \color{blue}{\left(x \cdot {t}^{2}\right)}\right)\right)\right) \]

   13. Simplified 51.8%

       \[\leadsto \color{blue}{y \cdot \left(0.5 \cdot \left(y \cdot \left(x \cdot \left(t \cdot t\right)\right)\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 45.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{+90}:\\ \;\;\;\;\frac{x}{y \cdot t + 1}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-133}:\\ \;\;\;\;x - b \cdot \left(x \cdot a\right)\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-32}:\\ \;\;\;\;\left(y \cdot y\right) \cdot \frac{x}{y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(0.5 \cdot \left(y \cdot \left(x \cdot \left(t \cdot t\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 32.4% accurate, 13.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.75 \cdot 10^{+90}:\\ \;\;\;\;\frac{x}{y \cdot t + 1}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-133}:\\ \;\;\;\;x - b \cdot \left(x \cdot a\right)\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-7}:\\ \;\;\;\;\left(y \cdot y\right) \cdot \frac{x}{y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(b \cdot \left(0 - a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -2.75e+90)
   (/ x (+ (* y t) 1.0))
   (if (<= y 1.9e-133)
     (- x (* b (* x a)))
     (if (<= y 4.2e-7) (* (* y y) (/ x (* y y))) (* x (* b (- 0.0 a)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.75e+90) {
		tmp = x / ((y * t) + 1.0);
	} else if (y <= 1.9e-133) {
		tmp = x - (b * (x * a));
	} else if (y <= 4.2e-7) {
		tmp = (y * y) * (x / (y * y));
	} else {
		tmp = x * (b * (0.0 - a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-2.75d+90)) then
        tmp = x / ((y * t) + 1.0d0)
    else if (y <= 1.9d-133) then
        tmp = x - (b * (x * a))
    else if (y <= 4.2d-7) then
        tmp = (y * y) * (x / (y * y))
    else
        tmp = x * (b * (0.0d0 - a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.75e+90) {
		tmp = x / ((y * t) + 1.0);
	} else if (y <= 1.9e-133) {
		tmp = x - (b * (x * a));
	} else if (y <= 4.2e-7) {
		tmp = (y * y) * (x / (y * y));
	} else {
		tmp = x * (b * (0.0 - a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -2.75e+90:
		tmp = x / ((y * t) + 1.0)
	elif y <= 1.9e-133:
		tmp = x - (b * (x * a))
	elif y <= 4.2e-7:
		tmp = (y * y) * (x / (y * y))
	else:
		tmp = x * (b * (0.0 - a))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -2.75e+90)
		tmp = Float64(x / Float64(Float64(y * t) + 1.0));
	elseif (y <= 1.9e-133)
		tmp = Float64(x - Float64(b * Float64(x * a)));
	elseif (y <= 4.2e-7)
		tmp = Float64(Float64(y * y) * Float64(x / Float64(y * y)));
	else
		tmp = Float64(x * Float64(b * Float64(0.0 - a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -2.75e+90)
		tmp = x / ((y * t) + 1.0);
	elseif (y <= 1.9e-133)
		tmp = x - (b * (x * a));
	elseif (y <= 4.2e-7)
		tmp = (y * y) * (x / (y * y));
	else
		tmp = x * (b * (0.0 - a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -2.75e+90], N[(x / N[(N[(y * t), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.9e-133], N[(x - N[(b * N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.2e-7], N[(N[(y * y), $MachinePrecision] * N[(x / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(b * N[(0.0 - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.74999999999999999e90

   1. Initial program 100.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(t \cdot y\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\left(y \cdot t\right)\right)\right) \]

      2. *-lowering-*.f64 72.1%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, t\right)\right)\right) \]

   7. Simplified 72.1%

      \[\leadsto \frac{x}{e^{\color{blue}{y \cdot t}}} \]

   8. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + t \cdot y\right)}\right) \]
   9. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(t \cdot y + \color{blue}{1}\right)\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\left(t \cdot y\right), \color{blue}{1}\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\left(y \cdot t\right), 1\right)\right) \]

      4. *-lowering-*.f64 39.7%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, t\right), 1\right)\right) \]

   10. Simplified 39.7%

       \[\leadsto \frac{x}{\color{blue}{y \cdot t + 1}} \]

   if -2.74999999999999999e90 < y < 1.9000000000000002e-133

   1. Initial program 94.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 94.0%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(a \cdot b\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 74.7%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, b\right)\right)\right) \]

   7. Simplified 74.7%

      \[\leadsto \frac{x}{e^{\color{blue}{a \cdot b}}} \]

   8. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + b \cdot \left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)\right)}\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(b \cdot \left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \color{blue}{\left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \color{blue}{\left(\frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right)\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(\left(\frac{1}{2} \cdot {a}^{2}\right) \cdot \color{blue}{b}\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\left(\frac{1}{2} \cdot {a}^{2}\right), \color{blue}{b}\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left({a}^{2}\right)\right), b\right)\right)\right)\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left(a \cdot a\right)\right), b\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 48.5%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(a, a\right)\right), b\right)\right)\right)\right)\right) \]

   10. Simplified 48.5%

       \[\leadsto \frac{x}{\color{blue}{1 + b \cdot \left(a + \left(0.5 \cdot \left(a \cdot a\right)\right) \cdot b\right)}} \]

   11. Taylor expanded in b around 0

       \[\leadsto \color{blue}{x + -1 \cdot \left(a \cdot \left(b \cdot x\right)\right)} \]
   12. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto x + \left(\mathsf{neg}\left(a \cdot \left(b \cdot x\right)\right)\right) \]

       2. unsub-neg N/A

          \[\leadsto x - \color{blue}{a \cdot \left(b \cdot x\right)} \]

       3. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(a \cdot \left(b \cdot x\right)\right)}\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(a, \color{blue}{\left(b \cdot x\right)}\right)\right) \]

       5. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(a, \left(x \cdot \color{blue}{b}\right)\right)\right) \]

       6. *-lowering-*.f64 37.8%

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(x, \color{blue}{b}\right)\right)\right) \]

   13. Simplified 37.8%

       \[\leadsto \color{blue}{x - a \cdot \left(x \cdot b\right)} \]
   14. Step-by-step derivation

       1. associate-*r* N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \left(\left(a \cdot x\right) \cdot \color{blue}{b}\right)\right) \]

       2. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\left(a \cdot x\right), \color{blue}{b}\right)\right) \]

       3. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\left(x \cdot a\right), b\right)\right) \]

       4. *-lowering-*.f64 40.8%

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, a\right), b\right)\right) \]

   15. Applied egg-rr 40.8%

       \[\leadsto x - \color{blue}{\left(x \cdot a\right) \cdot b} \]

   if 1.9000000000000002e-133 < y < 4.2e-7

   1. Initial program 96.3%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 96.4%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(t \cdot y\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\left(y \cdot t\right)\right)\right) \]

      2. *-lowering-*.f64 66.3%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, t\right)\right)\right) \]

   7. Simplified 66.3%

      \[\leadsto \frac{x}{e^{\color{blue}{y \cdot t}}} \]

   8. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x + y \cdot \left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) - t \cdot x\right)} \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot \left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) - t \cdot x\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) - t \cdot x\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right)\right), \color{blue}{\left(t \cdot x\right)}\right)\right)\right) \]

   10. Simplified 58.9%

       \[\leadsto \color{blue}{x + y \cdot \left(y \cdot \left(0.5 \cdot \left(x \cdot \left(t \cdot t\right)\right)\right) - x \cdot t\right)} \]

   11. Taylor expanded in y around -inf

       \[\leadsto \color{blue}{{y}^{2} \cdot \left(-1 \cdot \frac{-1 \cdot \frac{x}{y} + t \cdot x}{y} + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)} \]
   12. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left({y}^{2}\right), \color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{x}{y} + t \cdot x}{y} + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)}\right) \]

       2. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(y \cdot y\right), \left(\color{blue}{-1 \cdot \frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}} + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \left(\color{blue}{-1 \cdot \frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}} + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) \]

       4. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right) + \color{blue}{-1 \cdot \frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}}\right)\right) \]

       5. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right) + \left(\mathsf{neg}\left(\frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}\right)\right)\right)\right) \]

       6. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right) - \color{blue}{\frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}}\right)\right) \]

       7. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\left(\frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right), \color{blue}{\left(\frac{-1 \cdot \frac{x}{y} + t \cdot x}{y}\right)}\right)\right) \]

       8. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\left(\left({t}^{2} \cdot x\right) \cdot \frac{1}{2}\right), \left(\frac{\color{blue}{-1 \cdot \frac{x}{y} + t \cdot x}}{y}\right)\right)\right) \]

       9. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\left(\left(x \cdot {t}^{2}\right) \cdot \frac{1}{2}\right), \left(\frac{\color{blue}{-1 \cdot \frac{x}{y}} + t \cdot x}{y}\right)\right)\right) \]

       10. associate-*l* N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\left(x \cdot \left({t}^{2} \cdot \frac{1}{2}\right)\right), \left(\frac{\color{blue}{-1 \cdot \frac{x}{y} + t \cdot x}}{y}\right)\right)\right) \]

       11. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \left({t}^{2} \cdot \frac{1}{2}\right)\right), \left(\frac{\color{blue}{-1 \cdot \frac{x}{y} + t \cdot x}}{y}\right)\right)\right) \]

       12. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\left({t}^{2}\right), \frac{1}{2}\right)\right), \left(\frac{-1 \cdot \frac{x}{y} + \color{blue}{t \cdot x}}{y}\right)\right)\right) \]

       13. unpow2 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\left(t \cdot t\right), \frac{1}{2}\right)\right), \left(\frac{-1 \cdot \frac{x}{y} + \color{blue}{t} \cdot x}{y}\right)\right)\right) \]

       14. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, t\right), \frac{1}{2}\right)\right), \left(\frac{-1 \cdot \frac{x}{y} + \color{blue}{t} \cdot x}{y}\right)\right)\right) \]

       15. /-lowering-/.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(t, t\right), \frac{1}{2}\right)\right), \mathsf{/.f64}\left(\left(-1 \cdot \frac{x}{y} + t \cdot x\right), \color{blue}{y}\right)\right)\right) \]

   13. Simplified 65.7%

       \[\leadsto \color{blue}{\left(y \cdot y\right) \cdot \left(x \cdot \left(\left(t \cdot t\right) \cdot 0.5\right) - \frac{x \cdot t - \frac{x}{y}}{y}\right)} \]

   14. Taylor expanded in t around 0

       \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \color{blue}{\left(\frac{x}{{y}^{2}}\right)}\right) \]
   15. Step-by-step derivation

       1. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{/.f64}\left(x, \color{blue}{\left({y}^{2}\right)}\right)\right) \]

       2. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{/.f64}\left(x, \left(y \cdot \color{blue}{y}\right)\right)\right) \]

       3. *-lowering-*.f64 55.2%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, y\right), \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{y}\right)\right)\right) \]

   16. Simplified 55.2%

       \[\leadsto \left(y \cdot y\right) \cdot \color{blue}{\frac{x}{y \cdot y}} \]

   if 4.2e-7 < y

   1. Initial program 98.2%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 98.2%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(a \cdot b\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 30.2%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, b\right)\right)\right) \]

   7. Simplified 30.2%

      \[\leadsto \frac{x}{e^{\color{blue}{a \cdot b}}} \]

   8. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + b \cdot \left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)\right)}\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(b \cdot \left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \color{blue}{\left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \color{blue}{\left(\frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right)\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(\left(\frac{1}{2} \cdot {a}^{2}\right) \cdot \color{blue}{b}\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\left(\frac{1}{2} \cdot {a}^{2}\right), \color{blue}{b}\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left({a}^{2}\right)\right), b\right)\right)\right)\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left(a \cdot a\right)\right), b\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 21.3%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(a, a\right)\right), b\right)\right)\right)\right)\right) \]

   10. Simplified 21.3%

       \[\leadsto \frac{x}{\color{blue}{1 + b \cdot \left(a + \left(0.5 \cdot \left(a \cdot a\right)\right) \cdot b\right)}} \]

   11. Taylor expanded in b around 0

       \[\leadsto \color{blue}{x + -1 \cdot \left(a \cdot \left(b \cdot x\right)\right)} \]
   12. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto x + \left(\mathsf{neg}\left(a \cdot \left(b \cdot x\right)\right)\right) \]

       2. unsub-neg N/A

          \[\leadsto x - \color{blue}{a \cdot \left(b \cdot x\right)} \]

       3. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(a \cdot \left(b \cdot x\right)\right)}\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(a, \color{blue}{\left(b \cdot x\right)}\right)\right) \]

       5. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(a, \left(x \cdot \color{blue}{b}\right)\right)\right) \]

       6. *-lowering-*.f64 10.8%

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(x, \color{blue}{b}\right)\right)\right) \]

   13. Simplified 10.8%

       \[\leadsto \color{blue}{x - a \cdot \left(x \cdot b\right)} \]

   14. Taylor expanded in a around inf

       \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(b \cdot x\right)\right)} \]
   15. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \mathsf{neg}\left(a \cdot \left(b \cdot x\right)\right) \]

       2. neg-sub0 N/A

          \[\leadsto 0 - \color{blue}{a \cdot \left(b \cdot x\right)} \]

       3. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{\left(a \cdot \left(b \cdot x\right)\right)}\right) \]

       4. associate-*r* N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \left(\left(a \cdot b\right) \cdot \color{blue}{x}\right)\right) \]

       5. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \left(x \cdot \color{blue}{\left(a \cdot b\right)}\right)\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(x, \color{blue}{\left(a \cdot b\right)}\right)\right) \]

       7. *-lowering-*.f64 30.7%

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(a, \color{blue}{b}\right)\right)\right) \]

   16. Simplified 30.7%

       \[\leadsto \color{blue}{0 - x \cdot \left(a \cdot b\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 39.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.75 \cdot 10^{+90}:\\ \;\;\;\;\frac{x}{y \cdot t + 1}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-133}:\\ \;\;\;\;x - b \cdot \left(x \cdot a\right)\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-7}:\\ \;\;\;\;\left(y \cdot y\right) \cdot \frac{x}{y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(b \cdot \left(0 - a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 33.1% accurate, 18.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{+90}:\\ \;\;\;\;\frac{x}{y \cdot t + 1}\\ \mathbf{elif}\;y \leq 2.65:\\ \;\;\;\;x - b \cdot \left(x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(b \cdot \left(0 - a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.65e+90)
   (/ x (+ (* y t) 1.0))
   (if (<= y 2.65) (- x (* b (* x a))) (* x (* b (- 0.0 a))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.65e+90) {
		tmp = x / ((y * t) + 1.0);
	} else if (y <= 2.65) {
		tmp = x - (b * (x * a));
	} else {
		tmp = x * (b * (0.0 - a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-1.65d+90)) then
        tmp = x / ((y * t) + 1.0d0)
    else if (y <= 2.65d0) then
        tmp = x - (b * (x * a))
    else
        tmp = x * (b * (0.0d0 - a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.65e+90) {
		tmp = x / ((y * t) + 1.0);
	} else if (y <= 2.65) {
		tmp = x - (b * (x * a));
	} else {
		tmp = x * (b * (0.0 - a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.65e+90:
		tmp = x / ((y * t) + 1.0)
	elif y <= 2.65:
		tmp = x - (b * (x * a))
	else:
		tmp = x * (b * (0.0 - a))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.65e+90)
		tmp = Float64(x / Float64(Float64(y * t) + 1.0));
	elseif (y <= 2.65)
		tmp = Float64(x - Float64(b * Float64(x * a)));
	else
		tmp = Float64(x * Float64(b * Float64(0.0 - a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1.65e+90)
		tmp = x / ((y * t) + 1.0);
	elseif (y <= 2.65)
		tmp = x - (b * (x * a));
	else
		tmp = x * (b * (0.0 - a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.65e+90], N[(x / N[(N[(y * t), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.65], N[(x - N[(b * N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(b * N[(0.0 - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.65000000000000004e90

   1. Initial program 100.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(t \cdot y\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\left(y \cdot t\right)\right)\right) \]

      2. *-lowering-*.f64 72.1%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, t\right)\right)\right) \]

   7. Simplified 72.1%

      \[\leadsto \frac{x}{e^{\color{blue}{y \cdot t}}} \]

   8. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + t \cdot y\right)}\right) \]
   9. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(t \cdot y + \color{blue}{1}\right)\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\left(t \cdot y\right), \color{blue}{1}\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\left(y \cdot t\right), 1\right)\right) \]

      4. *-lowering-*.f64 39.7%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, t\right), 1\right)\right) \]

   10. Simplified 39.7%

       \[\leadsto \frac{x}{\color{blue}{y \cdot t + 1}} \]

   if -1.65000000000000004e90 < y < 2.64999999999999991

   1. Initial program 94.4%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 94.4%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(a \cdot b\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 72.3%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, b\right)\right)\right) \]

   7. Simplified 72.3%

      \[\leadsto \frac{x}{e^{\color{blue}{a \cdot b}}} \]

   8. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + b \cdot \left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)\right)}\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(b \cdot \left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \color{blue}{\left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \color{blue}{\left(\frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right)\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(\left(\frac{1}{2} \cdot {a}^{2}\right) \cdot \color{blue}{b}\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\left(\frac{1}{2} \cdot {a}^{2}\right), \color{blue}{b}\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left({a}^{2}\right)\right), b\right)\right)\right)\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left(a \cdot a\right)\right), b\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 45.1%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(a, a\right)\right), b\right)\right)\right)\right)\right) \]

   10. Simplified 45.1%

       \[\leadsto \frac{x}{\color{blue}{1 + b \cdot \left(a + \left(0.5 \cdot \left(a \cdot a\right)\right) \cdot b\right)}} \]

   11. Taylor expanded in b around 0

       \[\leadsto \color{blue}{x + -1 \cdot \left(a \cdot \left(b \cdot x\right)\right)} \]
   12. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto x + \left(\mathsf{neg}\left(a \cdot \left(b \cdot x\right)\right)\right) \]

       2. unsub-neg N/A

          \[\leadsto x - \color{blue}{a \cdot \left(b \cdot x\right)} \]

       3. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(a \cdot \left(b \cdot x\right)\right)}\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(a, \color{blue}{\left(b \cdot x\right)}\right)\right) \]

       5. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(a, \left(x \cdot \color{blue}{b}\right)\right)\right) \]

       6. *-lowering-*.f64 39.3%

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(x, \color{blue}{b}\right)\right)\right) \]

   13. Simplified 39.3%

       \[\leadsto \color{blue}{x - a \cdot \left(x \cdot b\right)} \]
   14. Step-by-step derivation

       1. associate-*r* N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \left(\left(a \cdot x\right) \cdot \color{blue}{b}\right)\right) \]

       2. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\left(a \cdot x\right), \color{blue}{b}\right)\right) \]

       3. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\left(x \cdot a\right), b\right)\right) \]

       4. *-lowering-*.f64 40.6%

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, a\right), b\right)\right) \]

   15. Applied egg-rr 40.6%

       \[\leadsto x - \color{blue}{\left(x \cdot a\right) \cdot b} \]

   if 2.64999999999999991 < y

   1. Initial program 98.2%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 98.2%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(a \cdot b\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 30.2%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, b\right)\right)\right) \]

   7. Simplified 30.2%

      \[\leadsto \frac{x}{e^{\color{blue}{a \cdot b}}} \]

   8. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + b \cdot \left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)\right)}\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(b \cdot \left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \color{blue}{\left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \color{blue}{\left(\frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right)\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(\left(\frac{1}{2} \cdot {a}^{2}\right) \cdot \color{blue}{b}\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\left(\frac{1}{2} \cdot {a}^{2}\right), \color{blue}{b}\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left({a}^{2}\right)\right), b\right)\right)\right)\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left(a \cdot a\right)\right), b\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 21.3%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(a, a\right)\right), b\right)\right)\right)\right)\right) \]

   10. Simplified 21.3%

       \[\leadsto \frac{x}{\color{blue}{1 + b \cdot \left(a + \left(0.5 \cdot \left(a \cdot a\right)\right) \cdot b\right)}} \]

   11. Taylor expanded in b around 0

       \[\leadsto \color{blue}{x + -1 \cdot \left(a \cdot \left(b \cdot x\right)\right)} \]
   12. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto x + \left(\mathsf{neg}\left(a \cdot \left(b \cdot x\right)\right)\right) \]

       2. unsub-neg N/A

          \[\leadsto x - \color{blue}{a \cdot \left(b \cdot x\right)} \]

       3. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(a \cdot \left(b \cdot x\right)\right)}\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(a, \color{blue}{\left(b \cdot x\right)}\right)\right) \]

       5. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(a, \left(x \cdot \color{blue}{b}\right)\right)\right) \]

       6. *-lowering-*.f64 10.8%

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(x, \color{blue}{b}\right)\right)\right) \]

   13. Simplified 10.8%

       \[\leadsto \color{blue}{x - a \cdot \left(x \cdot b\right)} \]

   14. Taylor expanded in a around inf

       \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(b \cdot x\right)\right)} \]
   15. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \mathsf{neg}\left(a \cdot \left(b \cdot x\right)\right) \]

       2. neg-sub0 N/A

          \[\leadsto 0 - \color{blue}{a \cdot \left(b \cdot x\right)} \]

       3. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{\left(a \cdot \left(b \cdot x\right)\right)}\right) \]

       4. associate-*r* N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \left(\left(a \cdot b\right) \cdot \color{blue}{x}\right)\right) \]

       5. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \left(x \cdot \color{blue}{\left(a \cdot b\right)}\right)\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(x, \color{blue}{\left(a \cdot b\right)}\right)\right) \]

       7. *-lowering-*.f64 30.7%

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(a, \color{blue}{b}\right)\right)\right) \]

   16. Simplified 30.7%

       \[\leadsto \color{blue}{0 - x \cdot \left(a \cdot b\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 38.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{+90}:\\ \;\;\;\;\frac{x}{y \cdot t + 1}\\ \mathbf{elif}\;y \leq 2.65:\\ \;\;\;\;x - b \cdot \left(x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(b \cdot \left(0 - a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 32.1% accurate, 18.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(b \cdot \left(0 - a\right)\right)\\ \mathbf{if}\;y \leq -4 \cdot 10^{-17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-5}:\\ \;\;\;\;x - b \cdot \left(x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (* b (- 0.0 a)))))
   (if (<= y -4e-17) t_1 (if (<= y 4e-5) (- x (* b (* x a))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (b * (0.0 - a));
	double tmp;
	if (y <= -4e-17) {
		tmp = t_1;
	} else if (y <= 4e-5) {
		tmp = x - (b * (x * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (b * (0.0d0 - a))
    if (y <= (-4d-17)) then
        tmp = t_1
    else if (y <= 4d-5) then
        tmp = x - (b * (x * a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (b * (0.0 - a));
	double tmp;
	if (y <= -4e-17) {
		tmp = t_1;
	} else if (y <= 4e-5) {
		tmp = x - (b * (x * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * (b * (0.0 - a))
	tmp = 0
	if y <= -4e-17:
		tmp = t_1
	elif y <= 4e-5:
		tmp = x - (b * (x * a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * Float64(b * Float64(0.0 - a)))
	tmp = 0.0
	if (y <= -4e-17)
		tmp = t_1;
	elseif (y <= 4e-5)
		tmp = Float64(x - Float64(b * Float64(x * a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * (b * (0.0 - a));
	tmp = 0.0;
	if (y <= -4e-17)
		tmp = t_1;
	elseif (y <= 4e-5)
		tmp = x - (b * (x * a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[(b * N[(0.0 - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4e-17], t$95$1, If[LessEqual[y, 4e-5], N[(x - N[(b * N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.00000000000000029e-17 or 4.00000000000000033e-5 < y

   1. Initial program 98.4%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 98.4%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(a \cdot b\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 32.6%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, b\right)\right)\right) \]

   7. Simplified 32.6%

      \[\leadsto \frac{x}{e^{\color{blue}{a \cdot b}}} \]

   8. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + b \cdot \left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)\right)}\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(b \cdot \left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \color{blue}{\left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \color{blue}{\left(\frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right)\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(\left(\frac{1}{2} \cdot {a}^{2}\right) \cdot \color{blue}{b}\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\left(\frac{1}{2} \cdot {a}^{2}\right), \color{blue}{b}\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left({a}^{2}\right)\right), b\right)\right)\right)\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left(a \cdot a\right)\right), b\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 21.0%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(a, a\right)\right), b\right)\right)\right)\right)\right) \]

   10. Simplified 21.0%

       \[\leadsto \frac{x}{\color{blue}{1 + b \cdot \left(a + \left(0.5 \cdot \left(a \cdot a\right)\right) \cdot b\right)}} \]

   11. Taylor expanded in b around 0

       \[\leadsto \color{blue}{x + -1 \cdot \left(a \cdot \left(b \cdot x\right)\right)} \]
   12. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto x + \left(\mathsf{neg}\left(a \cdot \left(b \cdot x\right)\right)\right) \]

       2. unsub-neg N/A

          \[\leadsto x - \color{blue}{a \cdot \left(b \cdot x\right)} \]

       3. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(a \cdot \left(b \cdot x\right)\right)}\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(a, \color{blue}{\left(b \cdot x\right)}\right)\right) \]

       5. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(a, \left(x \cdot \color{blue}{b}\right)\right)\right) \]

       6. *-lowering-*.f64 11.6%

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(x, \color{blue}{b}\right)\right)\right) \]

   13. Simplified 11.6%

       \[\leadsto \color{blue}{x - a \cdot \left(x \cdot b\right)} \]

   14. Taylor expanded in a around inf

       \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(b \cdot x\right)\right)} \]
   15. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \mathsf{neg}\left(a \cdot \left(b \cdot x\right)\right) \]

       2. neg-sub0 N/A

          \[\leadsto 0 - \color{blue}{a \cdot \left(b \cdot x\right)} \]

       3. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{\left(a \cdot \left(b \cdot x\right)\right)}\right) \]

       4. associate-*r* N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \left(\left(a \cdot b\right) \cdot \color{blue}{x}\right)\right) \]

       5. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \left(x \cdot \color{blue}{\left(a \cdot b\right)}\right)\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(x, \color{blue}{\left(a \cdot b\right)}\right)\right) \]

       7. *-lowering-*.f64 25.0%

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(a, \color{blue}{b}\right)\right)\right) \]

   16. Simplified 25.0%

       \[\leadsto \color{blue}{0 - x \cdot \left(a \cdot b\right)} \]

   if -4.00000000000000029e-17 < y < 4.00000000000000033e-5

   1. Initial program 94.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 94.0%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(a \cdot b\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 77.7%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, b\right)\right)\right) \]

   7. Simplified 77.7%

      \[\leadsto \frac{x}{e^{\color{blue}{a \cdot b}}} \]

   8. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + b \cdot \left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)\right)}\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(b \cdot \left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \color{blue}{\left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \color{blue}{\left(\frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right)\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(\left(\frac{1}{2} \cdot {a}^{2}\right) \cdot \color{blue}{b}\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\left(\frac{1}{2} \cdot {a}^{2}\right), \color{blue}{b}\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left({a}^{2}\right)\right), b\right)\right)\right)\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left(a \cdot a\right)\right), b\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 49.9%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(a, a\right)\right), b\right)\right)\right)\right)\right) \]

   10. Simplified 49.9%

       \[\leadsto \frac{x}{\color{blue}{1 + b \cdot \left(a + \left(0.5 \cdot \left(a \cdot a\right)\right) \cdot b\right)}} \]

   11. Taylor expanded in b around 0

       \[\leadsto \color{blue}{x + -1 \cdot \left(a \cdot \left(b \cdot x\right)\right)} \]
   12. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto x + \left(\mathsf{neg}\left(a \cdot \left(b \cdot x\right)\right)\right) \]

       2. unsub-neg N/A

          \[\leadsto x - \color{blue}{a \cdot \left(b \cdot x\right)} \]

       3. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(a \cdot \left(b \cdot x\right)\right)}\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(a, \color{blue}{\left(b \cdot x\right)}\right)\right) \]

       5. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(a, \left(x \cdot \color{blue}{b}\right)\right)\right) \]

       6. *-lowering-*.f64 43.5%

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(x, \color{blue}{b}\right)\right)\right) \]

   13. Simplified 43.5%

       \[\leadsto \color{blue}{x - a \cdot \left(x \cdot b\right)} \]
   14. Step-by-step derivation

       1. associate-*r* N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \left(\left(a \cdot x\right) \cdot \color{blue}{b}\right)\right) \]

       2. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\left(a \cdot x\right), \color{blue}{b}\right)\right) \]

       3. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\left(x \cdot a\right), b\right)\right) \]

       4. *-lowering-*.f64 45.8%

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(x, a\right), b\right)\right) \]

   15. Applied egg-rr 45.8%

       \[\leadsto x - \color{blue}{\left(x \cdot a\right) \cdot b} \]
3. Recombined 2 regimes into one program.

4. Final simplification 35.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-17}:\\ \;\;\;\;x \cdot \left(b \cdot \left(0 - a\right)\right)\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-5}:\\ \;\;\;\;x - b \cdot \left(x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(b \cdot \left(0 - a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 32.9% accurate, 18.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(b \cdot \left(0 - a\right)\right)\\ \mathbf{if}\;y \leq -1.75 \cdot 10^{-17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 0.044:\\ \;\;\;\;x - x \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (* b (- 0.0 a)))))
   (if (<= y -1.75e-17) t_1 (if (<= y 0.044) (- x (* x (* a b))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (b * (0.0 - a));
	double tmp;
	if (y <= -1.75e-17) {
		tmp = t_1;
	} else if (y <= 0.044) {
		tmp = x - (x * (a * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (b * (0.0d0 - a))
    if (y <= (-1.75d-17)) then
        tmp = t_1
    else if (y <= 0.044d0) then
        tmp = x - (x * (a * b))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (b * (0.0 - a));
	double tmp;
	if (y <= -1.75e-17) {
		tmp = t_1;
	} else if (y <= 0.044) {
		tmp = x - (x * (a * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * (b * (0.0 - a))
	tmp = 0
	if y <= -1.75e-17:
		tmp = t_1
	elif y <= 0.044:
		tmp = x - (x * (a * b))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * Float64(b * Float64(0.0 - a)))
	tmp = 0.0
	if (y <= -1.75e-17)
		tmp = t_1;
	elseif (y <= 0.044)
		tmp = Float64(x - Float64(x * Float64(a * b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * (b * (0.0 - a));
	tmp = 0.0;
	if (y <= -1.75e-17)
		tmp = t_1;
	elseif (y <= 0.044)
		tmp = x - (x * (a * b));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[(b * N[(0.0 - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.75e-17], t$95$1, If[LessEqual[y, 0.044], N[(x - N[(x * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.7500000000000001e-17 or 0.043999999999999997 < y

   1. Initial program 98.4%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 98.4%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(a \cdot b\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 32.6%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, b\right)\right)\right) \]

   7. Simplified 32.6%

      \[\leadsto \frac{x}{e^{\color{blue}{a \cdot b}}} \]

   8. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + b \cdot \left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)\right)}\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(b \cdot \left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \color{blue}{\left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \color{blue}{\left(\frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right)\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(\left(\frac{1}{2} \cdot {a}^{2}\right) \cdot \color{blue}{b}\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\left(\frac{1}{2} \cdot {a}^{2}\right), \color{blue}{b}\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left({a}^{2}\right)\right), b\right)\right)\right)\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left(a \cdot a\right)\right), b\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 21.0%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(a, a\right)\right), b\right)\right)\right)\right)\right) \]

   10. Simplified 21.0%

       \[\leadsto \frac{x}{\color{blue}{1 + b \cdot \left(a + \left(0.5 \cdot \left(a \cdot a\right)\right) \cdot b\right)}} \]

   11. Taylor expanded in b around 0

       \[\leadsto \color{blue}{x + -1 \cdot \left(a \cdot \left(b \cdot x\right)\right)} \]
   12. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto x + \left(\mathsf{neg}\left(a \cdot \left(b \cdot x\right)\right)\right) \]

       2. unsub-neg N/A

          \[\leadsto x - \color{blue}{a \cdot \left(b \cdot x\right)} \]

       3. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(a \cdot \left(b \cdot x\right)\right)}\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(a, \color{blue}{\left(b \cdot x\right)}\right)\right) \]

       5. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(a, \left(x \cdot \color{blue}{b}\right)\right)\right) \]

       6. *-lowering-*.f64 11.6%

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(x, \color{blue}{b}\right)\right)\right) \]

   13. Simplified 11.6%

       \[\leadsto \color{blue}{x - a \cdot \left(x \cdot b\right)} \]

   14. Taylor expanded in a around inf

       \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(b \cdot x\right)\right)} \]
   15. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \mathsf{neg}\left(a \cdot \left(b \cdot x\right)\right) \]

       2. neg-sub0 N/A

          \[\leadsto 0 - \color{blue}{a \cdot \left(b \cdot x\right)} \]

       3. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{\left(a \cdot \left(b \cdot x\right)\right)}\right) \]

       4. associate-*r* N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \left(\left(a \cdot b\right) \cdot \color{blue}{x}\right)\right) \]

       5. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \left(x \cdot \color{blue}{\left(a \cdot b\right)}\right)\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(x, \color{blue}{\left(a \cdot b\right)}\right)\right) \]

       7. *-lowering-*.f64 25.0%

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(a, \color{blue}{b}\right)\right)\right) \]

   16. Simplified 25.0%

       \[\leadsto \color{blue}{0 - x \cdot \left(a \cdot b\right)} \]

   if -1.7500000000000001e-17 < y < 0.043999999999999997

   1. Initial program 94.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 94.0%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(a \cdot b\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 77.7%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, b\right)\right)\right) \]

   7. Simplified 77.7%

      \[\leadsto \frac{x}{e^{\color{blue}{a \cdot b}}} \]

   8. Taylor expanded in a around 0

      \[\leadsto \color{blue}{x + -1 \cdot \left(a \cdot \left(b \cdot x\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto x + \left(\mathsf{neg}\left(a \cdot \left(b \cdot x\right)\right)\right) \]

      2. unsub-neg N/A

         \[\leadsto x - \color{blue}{a \cdot \left(b \cdot x\right)} \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(a \cdot \left(b \cdot x\right)\right)}\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\left(a \cdot b\right) \cdot \color{blue}{x}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\left(a \cdot b\right), \color{blue}{x}\right)\right) \]

      6. *-lowering-*.f64 45.0%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, b\right), x\right)\right) \]

   10. Simplified 45.0%

       \[\leadsto \color{blue}{x - \left(a \cdot b\right) \cdot x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 35.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{-17}:\\ \;\;\;\;x \cdot \left(b \cdot \left(0 - a\right)\right)\\ \mathbf{elif}\;y \leq 0.044:\\ \;\;\;\;x - x \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(b \cdot \left(0 - a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 31.9% accurate, 18.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(b \cdot \left(0 - a\right)\right)\\ \mathbf{if}\;y \leq -5 \cdot 10^{-17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-7}:\\ \;\;\;\;x - a \cdot \left(x \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (* b (- 0.0 a)))))
   (if (<= y -5e-17) t_1 (if (<= y 1.1e-7) (- x (* a (* x b))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (b * (0.0 - a));
	double tmp;
	if (y <= -5e-17) {
		tmp = t_1;
	} else if (y <= 1.1e-7) {
		tmp = x - (a * (x * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (b * (0.0d0 - a))
    if (y <= (-5d-17)) then
        tmp = t_1
    else if (y <= 1.1d-7) then
        tmp = x - (a * (x * b))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (b * (0.0 - a));
	double tmp;
	if (y <= -5e-17) {
		tmp = t_1;
	} else if (y <= 1.1e-7) {
		tmp = x - (a * (x * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * (b * (0.0 - a))
	tmp = 0
	if y <= -5e-17:
		tmp = t_1
	elif y <= 1.1e-7:
		tmp = x - (a * (x * b))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * Float64(b * Float64(0.0 - a)))
	tmp = 0.0
	if (y <= -5e-17)
		tmp = t_1;
	elseif (y <= 1.1e-7)
		tmp = Float64(x - Float64(a * Float64(x * b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * (b * (0.0 - a));
	tmp = 0.0;
	if (y <= -5e-17)
		tmp = t_1;
	elseif (y <= 1.1e-7)
		tmp = x - (a * (x * b));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[(b * N[(0.0 - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5e-17], t$95$1, If[LessEqual[y, 1.1e-7], N[(x - N[(a * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.9999999999999999e-17 or 1.1000000000000001e-7 < y

   1. Initial program 98.4%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 98.4%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(a \cdot b\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 32.6%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, b\right)\right)\right) \]

   7. Simplified 32.6%

      \[\leadsto \frac{x}{e^{\color{blue}{a \cdot b}}} \]

   8. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + b \cdot \left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)\right)}\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(b \cdot \left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \color{blue}{\left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \color{blue}{\left(\frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right)\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(\left(\frac{1}{2} \cdot {a}^{2}\right) \cdot \color{blue}{b}\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\left(\frac{1}{2} \cdot {a}^{2}\right), \color{blue}{b}\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left({a}^{2}\right)\right), b\right)\right)\right)\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left(a \cdot a\right)\right), b\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 21.0%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(a, a\right)\right), b\right)\right)\right)\right)\right) \]

   10. Simplified 21.0%

       \[\leadsto \frac{x}{\color{blue}{1 + b \cdot \left(a + \left(0.5 \cdot \left(a \cdot a\right)\right) \cdot b\right)}} \]

   11. Taylor expanded in b around 0

       \[\leadsto \color{blue}{x + -1 \cdot \left(a \cdot \left(b \cdot x\right)\right)} \]
   12. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto x + \left(\mathsf{neg}\left(a \cdot \left(b \cdot x\right)\right)\right) \]

       2. unsub-neg N/A

          \[\leadsto x - \color{blue}{a \cdot \left(b \cdot x\right)} \]

       3. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(a \cdot \left(b \cdot x\right)\right)}\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(a, \color{blue}{\left(b \cdot x\right)}\right)\right) \]

       5. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(a, \left(x \cdot \color{blue}{b}\right)\right)\right) \]

       6. *-lowering-*.f64 11.6%

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(x, \color{blue}{b}\right)\right)\right) \]

   13. Simplified 11.6%

       \[\leadsto \color{blue}{x - a \cdot \left(x \cdot b\right)} \]

   14. Taylor expanded in a around inf

       \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(b \cdot x\right)\right)} \]
   15. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \mathsf{neg}\left(a \cdot \left(b \cdot x\right)\right) \]

       2. neg-sub0 N/A

          \[\leadsto 0 - \color{blue}{a \cdot \left(b \cdot x\right)} \]

       3. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{\left(a \cdot \left(b \cdot x\right)\right)}\right) \]

       4. associate-*r* N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \left(\left(a \cdot b\right) \cdot \color{blue}{x}\right)\right) \]

       5. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \left(x \cdot \color{blue}{\left(a \cdot b\right)}\right)\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(x, \color{blue}{\left(a \cdot b\right)}\right)\right) \]

       7. *-lowering-*.f64 25.0%

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(a, \color{blue}{b}\right)\right)\right) \]

   16. Simplified 25.0%

       \[\leadsto \color{blue}{0 - x \cdot \left(a \cdot b\right)} \]

   if -4.9999999999999999e-17 < y < 1.1000000000000001e-7

   1. Initial program 94.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 94.0%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(a \cdot b\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 77.7%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, b\right)\right)\right) \]

   7. Simplified 77.7%

      \[\leadsto \frac{x}{e^{\color{blue}{a \cdot b}}} \]

   8. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + b \cdot \left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)\right)}\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(b \cdot \left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \color{blue}{\left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \color{blue}{\left(\frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right)\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(\left(\frac{1}{2} \cdot {a}^{2}\right) \cdot \color{blue}{b}\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\left(\frac{1}{2} \cdot {a}^{2}\right), \color{blue}{b}\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left({a}^{2}\right)\right), b\right)\right)\right)\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left(a \cdot a\right)\right), b\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 49.9%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(a, a\right)\right), b\right)\right)\right)\right)\right) \]

   10. Simplified 49.9%

       \[\leadsto \frac{x}{\color{blue}{1 + b \cdot \left(a + \left(0.5 \cdot \left(a \cdot a\right)\right) \cdot b\right)}} \]

   11. Taylor expanded in b around 0

       \[\leadsto \color{blue}{x + -1 \cdot \left(a \cdot \left(b \cdot x\right)\right)} \]
   12. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto x + \left(\mathsf{neg}\left(a \cdot \left(b \cdot x\right)\right)\right) \]

       2. unsub-neg N/A

          \[\leadsto x - \color{blue}{a \cdot \left(b \cdot x\right)} \]

       3. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(a \cdot \left(b \cdot x\right)\right)}\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(a, \color{blue}{\left(b \cdot x\right)}\right)\right) \]

       5. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(a, \left(x \cdot \color{blue}{b}\right)\right)\right) \]

       6. *-lowering-*.f64 43.5%

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(x, \color{blue}{b}\right)\right)\right) \]

   13. Simplified 43.5%

       \[\leadsto \color{blue}{x - a \cdot \left(x \cdot b\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 34.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-17}:\\ \;\;\;\;x \cdot \left(b \cdot \left(0 - a\right)\right)\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-7}:\\ \;\;\;\;x - a \cdot \left(x \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(b \cdot \left(0 - a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 28: 28.3% accurate, 18.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(b \cdot \left(0 - a\right)\right)\\ \mathbf{if}\;y \leq -1.95 \cdot 10^{-16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 0.003:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (* b (- 0.0 a)))))
   (if (<= y -1.95e-16) t_1 (if (<= y 0.003) x t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (b * (0.0 - a));
	double tmp;
	if (y <= -1.95e-16) {
		tmp = t_1;
	} else if (y <= 0.003) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (b * (0.0d0 - a))
    if (y <= (-1.95d-16)) then
        tmp = t_1
    else if (y <= 0.003d0) then
        tmp = x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (b * (0.0 - a));
	double tmp;
	if (y <= -1.95e-16) {
		tmp = t_1;
	} else if (y <= 0.003) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * (b * (0.0 - a))
	tmp = 0
	if y <= -1.95e-16:
		tmp = t_1
	elif y <= 0.003:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * Float64(b * Float64(0.0 - a)))
	tmp = 0.0
	if (y <= -1.95e-16)
		tmp = t_1;
	elseif (y <= 0.003)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * (b * (0.0 - a));
	tmp = 0.0;
	if (y <= -1.95e-16)
		tmp = t_1;
	elseif (y <= 0.003)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[(b * N[(0.0 - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.95e-16], t$95$1, If[LessEqual[y, 0.003], x, t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.94999999999999989e-16 or 0.0030000000000000001 < y

   1. Initial program 98.4%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 98.4%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(a \cdot b\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 32.6%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, b\right)\right)\right) \]

   7. Simplified 32.6%

      \[\leadsto \frac{x}{e^{\color{blue}{a \cdot b}}} \]

   8. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + b \cdot \left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)\right)}\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(b \cdot \left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \color{blue}{\left(a + \frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \color{blue}{\left(\frac{1}{2} \cdot \left({a}^{2} \cdot b\right)\right)}\right)\right)\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \left(\left(\frac{1}{2} \cdot {a}^{2}\right) \cdot \color{blue}{b}\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\left(\frac{1}{2} \cdot {a}^{2}\right), \color{blue}{b}\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left({a}^{2}\right)\right), b\right)\right)\right)\right)\right) \]

      7. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \left(a \cdot a\right)\right), b\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 21.0%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, \mathsf{*.f64}\left(a, a\right)\right), b\right)\right)\right)\right)\right) \]

   10. Simplified 21.0%

       \[\leadsto \frac{x}{\color{blue}{1 + b \cdot \left(a + \left(0.5 \cdot \left(a \cdot a\right)\right) \cdot b\right)}} \]

   11. Taylor expanded in b around 0

       \[\leadsto \color{blue}{x + -1 \cdot \left(a \cdot \left(b \cdot x\right)\right)} \]
   12. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto x + \left(\mathsf{neg}\left(a \cdot \left(b \cdot x\right)\right)\right) \]

       2. unsub-neg N/A

          \[\leadsto x - \color{blue}{a \cdot \left(b \cdot x\right)} \]

       3. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(a \cdot \left(b \cdot x\right)\right)}\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(a, \color{blue}{\left(b \cdot x\right)}\right)\right) \]

       5. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(a, \left(x \cdot \color{blue}{b}\right)\right)\right) \]

       6. *-lowering-*.f64 11.6%

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(x, \color{blue}{b}\right)\right)\right) \]

   13. Simplified 11.6%

       \[\leadsto \color{blue}{x - a \cdot \left(x \cdot b\right)} \]

   14. Taylor expanded in a around inf

       \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(b \cdot x\right)\right)} \]
   15. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \mathsf{neg}\left(a \cdot \left(b \cdot x\right)\right) \]

       2. neg-sub0 N/A

          \[\leadsto 0 - \color{blue}{a \cdot \left(b \cdot x\right)} \]

       3. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{\left(a \cdot \left(b \cdot x\right)\right)}\right) \]

       4. associate-*r* N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \left(\left(a \cdot b\right) \cdot \color{blue}{x}\right)\right) \]

       5. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \left(x \cdot \color{blue}{\left(a \cdot b\right)}\right)\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(x, \color{blue}{\left(a \cdot b\right)}\right)\right) \]

       7. *-lowering-*.f64 25.0%

          \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(a, \color{blue}{b}\right)\right)\right) \]

   16. Simplified 25.0%

       \[\leadsto \color{blue}{0 - x \cdot \left(a \cdot b\right)} \]

   if -1.94999999999999989e-16 < y < 0.0030000000000000001

   1. Initial program 94.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 94.0%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(a \cdot b\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 77.7%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, b\right)\right)\right) \]

   7. Simplified 77.7%

      \[\leadsto \frac{x}{e^{\color{blue}{a \cdot b}}} \]

   8. Taylor expanded in a around 0

      \[\leadsto \color{blue}{x} \]
   9. Step-by-step derivation

   10. Simplified 35.7%

       \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 30.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{-16}:\\ \;\;\;\;x \cdot \left(b \cdot \left(0 - a\right)\right)\\ \mathbf{elif}\;y \leq 0.003:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(b \cdot \left(0 - a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 29: 26.8% accurate, 18.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(x \cdot \left(0 - y\right)\right)\\ \mathbf{if}\;y \leq -1.35 \cdot 10^{-59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{-7}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (* x (- 0.0 y)))))
   (if (<= y -1.35e-59) t_1 (if (<= y 2.35e-7) x t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (x * (0.0 - y));
	double tmp;
	if (y <= -1.35e-59) {
		tmp = t_1;
	} else if (y <= 2.35e-7) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (x * (0.0d0 - y))
    if (y <= (-1.35d-59)) then
        tmp = t_1
    else if (y <= 2.35d-7) then
        tmp = x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (x * (0.0 - y));
	double tmp;
	if (y <= -1.35e-59) {
		tmp = t_1;
	} else if (y <= 2.35e-7) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (x * (0.0 - y))
	tmp = 0
	if y <= -1.35e-59:
		tmp = t_1
	elif y <= 2.35e-7:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(x * Float64(0.0 - y)))
	tmp = 0.0
	if (y <= -1.35e-59)
		tmp = t_1;
	elseif (y <= 2.35e-7)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (x * (0.0 - y));
	tmp = 0.0;
	if (y <= -1.35e-59)
		tmp = t_1;
	elseif (y <= 2.35e-7)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(x * N[(0.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.35e-59], t$95$1, If[LessEqual[y, 2.35e-7], x, t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.3499999999999999e-59 or 2.35e-7 < y

   1. Initial program 98.5%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 98.5%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(t \cdot y\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\left(y \cdot t\right)\right)\right) \]

      2. *-lowering-*.f64 59.0%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(y, t\right)\right)\right) \]

   7. Simplified 59.0%

      \[\leadsto \frac{x}{e^{\color{blue}{y \cdot t}}} \]

   8. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x + y \cdot \left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) - t \cdot x\right)} \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot \left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) - t \cdot x\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right) - t \cdot x\right)}\right)\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\left(-1 \cdot \left(y \cdot \left(-1 \cdot \left({t}^{2} \cdot x\right) + \frac{1}{2} \cdot \left({t}^{2} \cdot x\right)\right)\right)\right), \color{blue}{\left(t \cdot x\right)}\right)\right)\right) \]

   10. Simplified 21.0%

       \[\leadsto \color{blue}{x + y \cdot \left(y \cdot \left(0.5 \cdot \left(x \cdot \left(t \cdot t\right)\right)\right) - x \cdot t\right)} \]

   11. Taylor expanded in y around 0

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(-1 \cdot \left(t \cdot x\right)\right)}\right)\right) \]
   12. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \left(\mathsf{neg}\left(t \cdot x\right)\right)\right)\right) \]

       2. neg-sub0 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \left(0 - \color{blue}{t \cdot x}\right)\right)\right) \]

       3. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(0, \color{blue}{\left(t \cdot x\right)}\right)\right)\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(0, \left(x \cdot \color{blue}{t}\right)\right)\right)\right) \]

       5. *-lowering-*.f64 13.1%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(x, \color{blue}{t}\right)\right)\right)\right) \]

   13. Simplified 13.1%

       \[\leadsto x + y \cdot \color{blue}{\left(0 - x \cdot t\right)} \]

   14. Taylor expanded in y around inf

       \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(x \cdot y\right)\right)} \]
   15. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \mathsf{neg}\left(t \cdot \left(x \cdot y\right)\right) \]

       2. distribute-rgt-neg-in N/A

          \[\leadsto t \cdot \color{blue}{\left(\mathsf{neg}\left(x \cdot y\right)\right)} \]

       3. mul-1-neg N/A

          \[\leadsto t \cdot \left(-1 \cdot \color{blue}{\left(x \cdot y\right)}\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(-1 \cdot \left(x \cdot y\right)\right)}\right) \]

       5. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(t, \left(\mathsf{neg}\left(x \cdot y\right)\right)\right) \]

       6. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{*.f64}\left(t, \left(x \cdot \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right)\right) \]

       7. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(t, \left(x \cdot \left(-1 \cdot \color{blue}{y}\right)\right)\right) \]

       8. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(x, \color{blue}{\left(-1 \cdot y\right)}\right)\right) \]

       9. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(x, \left(\mathsf{neg}\left(y\right)\right)\right)\right) \]

       10. neg-lowering-neg.f64 15.0%

           \[\leadsto \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(x, \mathsf{neg.f64}\left(y\right)\right)\right) \]

   16. Simplified 15.0%

       \[\leadsto \color{blue}{t \cdot \left(x \cdot \left(-y\right)\right)} \]

   if -1.3499999999999999e-59 < y < 2.35e-7

   1. Initial program 93.7%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

   3. Simplified 93.7%

      \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(a \cdot b\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 78.4%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, b\right)\right)\right) \]

   7. Simplified 78.4%

      \[\leadsto \frac{x}{e^{\color{blue}{a \cdot b}}} \]

   8. Taylor expanded in a around 0

      \[\leadsto \color{blue}{x} \]
   9. Step-by-step derivation

   10. Simplified 36.9%

       \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 25.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{-59}:\\ \;\;\;\;t \cdot \left(x \cdot \left(0 - y\right)\right)\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{-7}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(x \cdot \left(0 - y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 30: 19.9% accurate, 315.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 x)

C

double code(double x, double y, double z, double t, double a, double b) {
	return x;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = x
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return x;
}

Python

def code(x, y, z, t, a, b):
	return x

Julia

function code(x, y, z, t, a, b)
	return x
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := x

Derivation

1. Initial program 96.2%

   \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]

3. Simplified 96.2%

   \[\leadsto \color{blue}{\frac{x}{e^{a \cdot \left(b - \log \left(1 - z\right)\right) + y \cdot \left(t - \log z\right)}}} \]
4. Add Preprocessing

5. Taylor expanded in b around inf

   \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\color{blue}{\left(a \cdot b\right)}\right)\right) \]
6. Step-by-step derivation

   1. *-lowering-*.f64 55.5%

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(a, b\right)\right)\right) \]

7. Simplified 55.5%

   \[\leadsto \frac{x}{e^{\color{blue}{a \cdot b}}} \]

8. Taylor expanded in a around 0

   \[\leadsto \color{blue}{x} \]
9. Step-by-step derivation

10. Simplified 20.3%

    \[\leadsto \color{blue}{x} \]
11. Add Preprocessing

Reproduce

herbie shell --seed 2024155 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:incompleteBetaApprox from math-functions-0.1.5.2, B"
  :precision binary64
  (* x (exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))))